Marwan Darwish | American University of Beirut (original) (raw)

Papers by Marwan Darwish

Numerical Heat Transfer, Part B: Fundamentals, 2020

This article deals with the development of an implicit and conservative method for conjugate heat... more This article deals with the development of an implicit and conservative method for conjugate heat transfer at solid-fluid interfaces. The technique is applicable for both conformal and non-conformal meshes. The method, which is implemented within a fully coupled in-house code, is symmetric in its treatment of the solid and fluid regions and is shown to be very robust for highly complex configurations. To demonstrate the performance of the method, two compressible turbulent conjugate heat transfer test cases, the Mark II and C3X with film cooling, which are benchmarks for simulating the hydrodynamic and thermal fields around and inside turbine blades, are used. Numerical results generated are in good agreement with available experimental measurements.

Fluid Mechanics and Its Applications, 2015

So far, the discretization of the general steady diffusion equation has been formulated on orthog... more So far, the discretization of the general steady diffusion equation has been formulated on orthogonal, non-orthogonal, structured, and unstructured grids. Another important term, the convection term represented by the divergence operator, is the focus of this chapter. Initially this term is discretized using a symmetrical linear profile similar to the one adopted for the discretization of the diffusion term. The shortcomings of this profile are delineated and a remedy is suggested through the use of an upwind profile. Even though it leads to physically plausible predictions, the upwind profile is shown to be highly diffusive generating results that are first order accurate. To increase accuracy, higher order profiles that are upwind biased are introduced. While reducing the discretization error, higher order profiles are shown to give rise to another type of error known as the dispersion error. Methods dealing with this error will be dealt with in the next chapter. Moreover, the flow field, which represents the driving catalyst of the convection term, is assumed to be known. The computation of the flow field will be the subject of later chapters.

Fluid Mechanics and Its Applications, 2015

AIP Conference Proceedings, 2010

ABSTRACT The efficient solution of flow problems depends on quality meshing the computational dom... more ABSTRACT The efficient solution of flow problems depends on quality meshing the computational domain. In problems with complex geometries or having a large spectrum of time or length scale, the meshing process greatly benefits from the subdivision of the original geometry (domain decomposition) into sub-domains, that are meshed independently with suitable elements and mesh density. Procedures for solving multiblock meshes can be of two types explicit or implicit. In either case it is essential that the fluxes at the regions interfaces be conserved. In this paper an efficient fully implicit multi-region coupling discretization procedure is presented. A test problem involving 1, 2, 4 and 8 blocks with a mesh size of about 100,000 elements, is solved to show that the coupling procedure yields the same number of iteration for multiple block as for a single block.

Numerical Heat Transfer, Part B: Fundamentals, 1998

ABSTRACT The family of skew very high resolution (VHR) schemes is adoptively combined with the fa... more ABSTRACT The family of skew very high resolution (VHR) schemes is adoptively combined with the family of high-resolution (HR) schemes to yield a new family of adaptive very high resolution (AVHR) schemes. A new simple adaptive switching criterion is devised. For convection-diffusion type problems the adaptive schemes are accelerated by using in tandem the normalized weighting factor method to implement the HR scheme and the deferred-correction (DC) procedure to implement the skew scheme. For flow problems the DC procedure is used to implement both types of schemes. Numerical results for the new family of AVHR schemes are compared in terms of accuracy and computation cost against those generated using the VHR base family of schemes by solving four problems: (1) pure convection of a step profile in an oblique velocity field, (2) driven flow in a skew cavity, (3) laminar sudden expansion of an oblique velocity field in a rectangular cavity, (4) and turbulent sudden expansion of an oblique velocity field in a rectangular cavity. For the same accuracy, the AVHR schemes are found to decrease the computation cost, on average, by 48.74% as compared to the VHR schemes.

Numerical Heat Transfer, Part A: Applications, 1995

ABSTRACT The influence of wall heat conduction on laminar mixed convection in externally finned v... more ABSTRACT The influence of wall heat conduction on laminar mixed convection in externally finned vertical pipes are investigated numerically. Buoyancy in both aiding and opposed modes is considered. Results are presented in terms of the streamwise variation of the fluid bulk temperature and tube-side Nusselt number, axially averaged and periodically fully developed Nusselt number values, and axial velocity and temperature profiles. For opposed flows, buoyancy forces decrease the overall heat transferred to the fluid, while for buoyancy-aided flows, buoyancy causes an enhancement in the overall heat transferred to the fluid. Inclusion of longitudinal wall conduction increases the heat transfer to the fluid and enhances the effects of buoyancy.

Numerical Heat Transfer, Part A: Applications, 2010

Numerical solutions are presented for laminar natural convection heat transfer in a fluid saturat... more Numerical solutions are presented for laminar natural convection heat transfer in a fluid saturated porous enclosure between two isothermal concentric cylinders of rhombic cross-sections. Simulations are conducted for four values of Raleigh number (Ra = 104, 105, 106, and 107), three values of Darcy number (Da = 10−1, 10−3, and 10−5), three values of porosity (ϵ = 0.3, 0.6, and 0.9), four values of enclosure gap (E g = 0.875, 0.75, 0.5, and 0.25), and two values of Prandtl number (Pr = 0.7 and 5). The results are reported in terms of streamlines, isotherms, mid-height velocity and temperature profiles, and local and average Nusselt number values. The flow strength and convection heat transfer increase with an increase in Ra, Da, E g , and/or ϵ. At low E g values, the flow in the enclosure is weak and convection heat transfer is low even though the total heat transfer is higher than at higher E g values, due to an increase in conduction heat transfer. An increase in Pr is associated with a decrease in the flow strength and an increase in total heat transfer. Furthermore, predictions indicate the presence of a critical Ra number below which conduction is the dominant heat transfer mode. Convection starts affecting the total heat transfer at Ra values higher than the critical one. The critical Ra decreases with increasing Da and/or ϵ, and increases with decreasing E g .

Applied Mathematics and Computation, 2011

This paper reports on the use of the Normalized Weighting Factor (NWF) method and the Deferred Co... more This paper reports on the use of the Normalized Weighting Factor (NWF) method and the Deferred Correction (DC) approach for the implementation of High Resolution (HR) convective schemes in an implicit, fully coupled, pressure-based flow solver. Four HR ...

INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020

The current work presents necessary geometric modifications to the coarse grids utilized in a ful... more The current work presents necessary geometric modifications to the coarse grids utilized in a full approximation scheme method (FAS). This work path is a preliminary stage to the development of a robust full approximation scheme method which withstand high distortions in the coarse grids of the grid hierarchy. The hierarchies of coarse grids required by the FAS method are commonly constructed using low-quality agglomeration algorithms that deteriorate performance. This work attempts to resolve the problem by altering the agglomeration procedure through a geometric modification to the coarse cells. While the proposed method does not require any complicated or time-consuming agglomeration techniques, its turnout has enhanced the solver stability.

The paper deals with assessing the performance of three algorithms (full multiphase, MUSIG, and H... more The paper deals with assessing the performance of three algorithms (full multiphase, MUSIG, and H-MUSIG) for the simulation of mixing and evaporation of droplets injected into a stream flowing at supersonic speeds. All algorithms, implemented within a finite volume method, use an Eulerian pressure-based formulation but differ in the representation of the disperse phase. In the full multiphase approach each droplet size is considered a phase with a phasic velocity, energy, and volume fraction equation. In the MUSIG model, there is only one disperse phase that is decomposed into N size groups, all moving at the same speed. To account for each size group, a size fraction equation is solved. The H-MUSIG model can be viewed as a blend between the full multi-phase approach and the two-phase MUSIG approach by subdividing droplets into classes with droplet size groups in each class sharing the same velocity. Turbulence in the gas phase is accounted for by using the k-ε two-equation model wh...

The Finite Volume Method in Computational Fluid Dynamics, 2015

The implementation of the finite volume mesh can follow many directions whether in the definition... more The implementation of the finite volume mesh can follow many directions whether in the definition of the mesh fields, the storing of the variables, or even in determining the connectivity relations. This chapter aims at outlining the design decisions that shape the implementation of two CFD codes, uFVM an educational unstructured Finite Volume code and OpenFOAM ® an industrialstrength open source code. The two codes are thus presented, initially in terms of their data structure and memory management schemes, and then in terms of how cases are setup. Finally the format of the system of equations generated by each of the two codes are detailed. The reader will notice that while uFVM shares many of the implementation details with OpenFOAM ® , its simplicity allows for the use of simpler implementation techniques and data structure. 7.1 uFVM The unstructured finite volume code uFVM was written to illustrate the various numerical techniques and algorithms, which collectively form a CFD program. Furthermore its numerics are in many ways similar to those in OpenFOAM ® [1], making it a good vehicle to understand and present the internals of OpenFOAM ®. The main data structures used in uFVM generally mirrors those in OpenFOAM ® especially in terms of mesh fields and boundary conditions. Still differences between uFVM and OpenFOAM ® will be used to underline various options available to CFD coders and thus to better present some implementation details. 7.1.1 An OpenFOAM ® Test Case The uFVM code is capable of reading an OpenFOAM ® mesh included as part of any OpenFOAM ® test case. An OpenFOAM ® test case is a directory that generally

In this work three approaches for the simulation of droplet mixing and evaporation using the Eule... more In this work three approaches for the simulation of droplet mixing and evaporation using the Eulerian approach are presented and compared. The implemented algorithms are (a) a full multiphase flow model where droplets of various group sizes are treated as separate disperse flow phases, (b) the Multi-Size Group Model (MUSIG) where the various droplet group sizes are assumed to share the same velocity and temperature field and some averaged drag coefficient is computed based on the various droplet sizes, and finally (c) the Heterogeneous Multi-Size Group Model (H-MUSIG) is presented, the model offers the best of the above two approaches. In all three approaches droplet break up, coalescence [3,4] and evaporation are accounted for, with droplets moving from one size group to another. The various models are implemented within a pressurebased finite volume flow solver. The k-H model is used to model turbulence in the gas phase while an algebraic model is used for the disperse phase. Resu...

Numerical Heat Transfer, Part A: Applications, 2017

A numerical investigation is conducted to study the performance of solar wind energy towers. The ... more A numerical investigation is conducted to study the performance of solar wind energy towers. The two-phase flow of air and water droplets in the tower is modeled following an Euler–Lagrange approach with air representing the continuous phase and water droplets the discrete phase. Results demonstrate that energy towers perform best in hot and dry environments. Water injection at the inlet to a tower increases the strength of the downdraft current with the rate of increase diminishing as the flow at exit approaches saturation. At a given water injection rate and tower diameter the downdraft strength increases as the height increases, while it is independent of the diameter at constant height. Energy analysis shows that for towers of low height the cost of electricity is expensive and commercially unfeasible, while it is cheap for towers of heights higher than 100 m.

Fluid Mechanics and Its Applications, 2015

Computational Fluid Dynamics 2006, 2009

This paper deals with the implementation and performance analysis of a parallel Algebraic Multigr... more This paper deals with the implementation and performance analysis of a parallel Algebraic Multigrid Solver (pAMG) for a finite volume unstructured CFD code. The parallelization of the solver is based on the domain decomposition approach using the single program multiple data paradigm. The Message passing interface Library (MPI) is used for communication of data. An ILU(0) iterative solver is used for smoothing the errors arising within each partition at the different grid levels, and a multi-level synchronization across the computational domain partitions is enforced in order to improve the performance of the parallelized Multigrid solver. Two synchronization strategies are evaluated: in the first the synchronization is applied across the multigrid levels during the restriction step in addition to the base level, while in the second the synchronization is enforced during the restriction and prolongation steps. To increase robustness gathering of coefficients across partitions for the coarsest level is investigated. Tests on a number of grids from 100,00 to 800,000 elements for diffusion and advection problems have been conducted on up to 20 processors.

International Journal of Mechanical Engineering Education, 1996

This paper describes IDGG, an Interactive Dynamic Grid Generator, for use as an educational tool ... more This paper describes IDGG, an Interactive Dynamic Grid Generator, for use as an educational tool by students studying computational fluid dynamics. The package is a Windows applications and runs on IBM PC, or compatible, computers. It is written in Pascal and built using object-oriented programming. The computer program allows the user to generate boundary-fitted curvilinear grids in any two-dimensional domain. The procedure adopted requires the user to perform the transformation step by step allowing him/her to easily grasp the concept of boundary-fitted coordinate systems. In addition, IDGG may be used by CFD researchers to display results graphically in the form of vector fields, contours, and two- and three-dimensional plots. The examples provided show the effectiveness of the package as a teaching aid.

Numerical Heat Transfer, Part B: Fundamentals, 2014

The paper deals with assessing the performance of three algorithms (full multiphase, MUSIG, and H... more The paper deals with assessing the performance of three algorithms (full multiphase, MUSIG, and H-MUSIG) for the simulation of mixing and evaporation of droplets injected into a stream flowing at supersonic speeds. All algorithms, implemented within a finite volume method, use an Eulerian pressure-based formulation but differ in the representation of the disperse phase. In the full multiphase approach each

Physics of Fluids, 2008

This paper deals with the formulation, implementation, and testing of three numerical techniques ... more This paper deals with the formulation, implementation, and testing of three numerical techniques based on (i) a full multiphase approach, (ii) a MUlti-SIze Group (MUSIG) approach, and (iii) a Heterogeneous MUSIG (H-MUSIG) approach for the prediction of mixing and evaporation of liquid droplets injected into a stream of air. The numerical procedures are formulated following an Eulerian approach, within a pressure-based fully conservative Finite Volume method equally applicable in the subsonic, transonic, and supersonic regimes, for the discrete and continuous phases. The k-ε two-equation turbulence model is used to account for the droplet and gas turbulence with modifications to account for compressibility at high speeds. The performances of the various methods are compared by solving for two configurations involving stream-wise and cross-stream spraying into subsonic and supersonic streams. Results, displayed in the form of droplet velocity vectors, contour plots, and axial profiles indicate that solutions obtained by the various techniques exhibit similar behavior. Differences in values are relatively small with the largest being associated with droplet volume fractions and vapor mass fraction in the gas phase. This is attributed to the fact that with MUSIG and H-MUSIG no droplet diameter equation is solved and the diameter of the various droplet phases are held constant, as opposed to the full multiphase approach.

Numerical Heat Transfer, Part B: Fundamentals, 2020

This article deals with the development of an implicit and conservative method for conjugate heat... more This article deals with the development of an implicit and conservative method for conjugate heat transfer at solid-fluid interfaces. The technique is applicable for both conformal and non-conformal meshes. The method, which is implemented within a fully coupled in-house code, is symmetric in its treatment of the solid and fluid regions and is shown to be very robust for highly complex configurations. To demonstrate the performance of the method, two compressible turbulent conjugate heat transfer test cases, the Mark II and C3X with film cooling, which are benchmarks for simulating the hydrodynamic and thermal fields around and inside turbine blades, are used. Numerical results generated are in good agreement with available experimental measurements.

Fluid Mechanics and Its Applications, 2015

So far, the discretization of the general steady diffusion equation has been formulated on orthog... more So far, the discretization of the general steady diffusion equation has been formulated on orthogonal, non-orthogonal, structured, and unstructured grids. Another important term, the convection term represented by the divergence operator, is the focus of this chapter. Initially this term is discretized using a symmetrical linear profile similar to the one adopted for the discretization of the diffusion term. The shortcomings of this profile are delineated and a remedy is suggested through the use of an upwind profile. Even though it leads to physically plausible predictions, the upwind profile is shown to be highly diffusive generating results that are first order accurate. To increase accuracy, higher order profiles that are upwind biased are introduced. While reducing the discretization error, higher order profiles are shown to give rise to another type of error known as the dispersion error. Methods dealing with this error will be dealt with in the next chapter. Moreover, the flow field, which represents the driving catalyst of the convection term, is assumed to be known. The computation of the flow field will be the subject of later chapters.

Fluid Mechanics and Its Applications, 2015

AIP Conference Proceedings, 2010

ABSTRACT The efficient solution of flow problems depends on quality meshing the computational dom... more ABSTRACT The efficient solution of flow problems depends on quality meshing the computational domain. In problems with complex geometries or having a large spectrum of time or length scale, the meshing process greatly benefits from the subdivision of the original geometry (domain decomposition) into sub-domains, that are meshed independently with suitable elements and mesh density. Procedures for solving multiblock meshes can be of two types explicit or implicit. In either case it is essential that the fluxes at the regions interfaces be conserved. In this paper an efficient fully implicit multi-region coupling discretization procedure is presented. A test problem involving 1, 2, 4 and 8 blocks with a mesh size of about 100,000 elements, is solved to show that the coupling procedure yields the same number of iteration for multiple block as for a single block.

Numerical Heat Transfer, Part B: Fundamentals, 1998

ABSTRACT The family of skew very high resolution (VHR) schemes is adoptively combined with the fa... more ABSTRACT The family of skew very high resolution (VHR) schemes is adoptively combined with the family of high-resolution (HR) schemes to yield a new family of adaptive very high resolution (AVHR) schemes. A new simple adaptive switching criterion is devised. For convection-diffusion type problems the adaptive schemes are accelerated by using in tandem the normalized weighting factor method to implement the HR scheme and the deferred-correction (DC) procedure to implement the skew scheme. For flow problems the DC procedure is used to implement both types of schemes. Numerical results for the new family of AVHR schemes are compared in terms of accuracy and computation cost against those generated using the VHR base family of schemes by solving four problems: (1) pure convection of a step profile in an oblique velocity field, (2) driven flow in a skew cavity, (3) laminar sudden expansion of an oblique velocity field in a rectangular cavity, (4) and turbulent sudden expansion of an oblique velocity field in a rectangular cavity. For the same accuracy, the AVHR schemes are found to decrease the computation cost, on average, by 48.74% as compared to the VHR schemes.

Numerical Heat Transfer, Part A: Applications, 1995

ABSTRACT The influence of wall heat conduction on laminar mixed convection in externally finned v... more ABSTRACT The influence of wall heat conduction on laminar mixed convection in externally finned vertical pipes are investigated numerically. Buoyancy in both aiding and opposed modes is considered. Results are presented in terms of the streamwise variation of the fluid bulk temperature and tube-side Nusselt number, axially averaged and periodically fully developed Nusselt number values, and axial velocity and temperature profiles. For opposed flows, buoyancy forces decrease the overall heat transferred to the fluid, while for buoyancy-aided flows, buoyancy causes an enhancement in the overall heat transferred to the fluid. Inclusion of longitudinal wall conduction increases the heat transfer to the fluid and enhances the effects of buoyancy.

Numerical Heat Transfer, Part A: Applications, 2010

Numerical solutions are presented for laminar natural convection heat transfer in a fluid saturat... more Numerical solutions are presented for laminar natural convection heat transfer in a fluid saturated porous enclosure between two isothermal concentric cylinders of rhombic cross-sections. Simulations are conducted for four values of Raleigh number (Ra = 104, 105, 106, and 107), three values of Darcy number (Da = 10−1, 10−3, and 10−5), three values of porosity (ϵ = 0.3, 0.6, and 0.9), four values of enclosure gap (E g = 0.875, 0.75, 0.5, and 0.25), and two values of Prandtl number (Pr = 0.7 and 5). The results are reported in terms of streamlines, isotherms, mid-height velocity and temperature profiles, and local and average Nusselt number values. The flow strength and convection heat transfer increase with an increase in Ra, Da, E g , and/or ϵ. At low E g values, the flow in the enclosure is weak and convection heat transfer is low even though the total heat transfer is higher than at higher E g values, due to an increase in conduction heat transfer. An increase in Pr is associated with a decrease in the flow strength and an increase in total heat transfer. Furthermore, predictions indicate the presence of a critical Ra number below which conduction is the dominant heat transfer mode. Convection starts affecting the total heat transfer at Ra values higher than the critical one. The critical Ra decreases with increasing Da and/or ϵ, and increases with decreasing E g .

Applied Mathematics and Computation, 2011

This paper reports on the use of the Normalized Weighting Factor (NWF) method and the Deferred Co... more This paper reports on the use of the Normalized Weighting Factor (NWF) method and the Deferred Correction (DC) approach for the implementation of High Resolution (HR) convective schemes in an implicit, fully coupled, pressure-based flow solver. Four HR ...

INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020

The current work presents necessary geometric modifications to the coarse grids utilized in a ful... more The current work presents necessary geometric modifications to the coarse grids utilized in a full approximation scheme method (FAS). This work path is a preliminary stage to the development of a robust full approximation scheme method which withstand high distortions in the coarse grids of the grid hierarchy. The hierarchies of coarse grids required by the FAS method are commonly constructed using low-quality agglomeration algorithms that deteriorate performance. This work attempts to resolve the problem by altering the agglomeration procedure through a geometric modification to the coarse cells. While the proposed method does not require any complicated or time-consuming agglomeration techniques, its turnout has enhanced the solver stability.

The paper deals with assessing the performance of three algorithms (full multiphase, MUSIG, and H... more The paper deals with assessing the performance of three algorithms (full multiphase, MUSIG, and H-MUSIG) for the simulation of mixing and evaporation of droplets injected into a stream flowing at supersonic speeds. All algorithms, implemented within a finite volume method, use an Eulerian pressure-based formulation but differ in the representation of the disperse phase. In the full multiphase approach each droplet size is considered a phase with a phasic velocity, energy, and volume fraction equation. In the MUSIG model, there is only one disperse phase that is decomposed into N size groups, all moving at the same speed. To account for each size group, a size fraction equation is solved. The H-MUSIG model can be viewed as a blend between the full multi-phase approach and the two-phase MUSIG approach by subdividing droplets into classes with droplet size groups in each class sharing the same velocity. Turbulence in the gas phase is accounted for by using the k-ε two-equation model wh...

The Finite Volume Method in Computational Fluid Dynamics, 2015

The implementation of the finite volume mesh can follow many directions whether in the definition... more The implementation of the finite volume mesh can follow many directions whether in the definition of the mesh fields, the storing of the variables, or even in determining the connectivity relations. This chapter aims at outlining the design decisions that shape the implementation of two CFD codes, uFVM an educational unstructured Finite Volume code and OpenFOAM ® an industrialstrength open source code. The two codes are thus presented, initially in terms of their data structure and memory management schemes, and then in terms of how cases are setup. Finally the format of the system of equations generated by each of the two codes are detailed. The reader will notice that while uFVM shares many of the implementation details with OpenFOAM ® , its simplicity allows for the use of simpler implementation techniques and data structure. 7.1 uFVM The unstructured finite volume code uFVM was written to illustrate the various numerical techniques and algorithms, which collectively form a CFD program. Furthermore its numerics are in many ways similar to those in OpenFOAM ® [1], making it a good vehicle to understand and present the internals of OpenFOAM ®. The main data structures used in uFVM generally mirrors those in OpenFOAM ® especially in terms of mesh fields and boundary conditions. Still differences between uFVM and OpenFOAM ® will be used to underline various options available to CFD coders and thus to better present some implementation details. 7.1.1 An OpenFOAM ® Test Case The uFVM code is capable of reading an OpenFOAM ® mesh included as part of any OpenFOAM ® test case. An OpenFOAM ® test case is a directory that generally

In this work three approaches for the simulation of droplet mixing and evaporation using the Eule... more In this work three approaches for the simulation of droplet mixing and evaporation using the Eulerian approach are presented and compared. The implemented algorithms are (a) a full multiphase flow model where droplets of various group sizes are treated as separate disperse flow phases, (b) the Multi-Size Group Model (MUSIG) where the various droplet group sizes are assumed to share the same velocity and temperature field and some averaged drag coefficient is computed based on the various droplet sizes, and finally (c) the Heterogeneous Multi-Size Group Model (H-MUSIG) is presented, the model offers the best of the above two approaches. In all three approaches droplet break up, coalescence [3,4] and evaporation are accounted for, with droplets moving from one size group to another. The various models are implemented within a pressurebased finite volume flow solver. The k-H model is used to model turbulence in the gas phase while an algebraic model is used for the disperse phase. Resu...

Numerical Heat Transfer, Part A: Applications, 2017

A numerical investigation is conducted to study the performance of solar wind energy towers. The ... more A numerical investigation is conducted to study the performance of solar wind energy towers. The two-phase flow of air and water droplets in the tower is modeled following an Euler–Lagrange approach with air representing the continuous phase and water droplets the discrete phase. Results demonstrate that energy towers perform best in hot and dry environments. Water injection at the inlet to a tower increases the strength of the downdraft current with the rate of increase diminishing as the flow at exit approaches saturation. At a given water injection rate and tower diameter the downdraft strength increases as the height increases, while it is independent of the diameter at constant height. Energy analysis shows that for towers of low height the cost of electricity is expensive and commercially unfeasible, while it is cheap for towers of heights higher than 100 m.

Fluid Mechanics and Its Applications, 2015

Computational Fluid Dynamics 2006, 2009

This paper deals with the implementation and performance analysis of a parallel Algebraic Multigr... more This paper deals with the implementation and performance analysis of a parallel Algebraic Multigrid Solver (pAMG) for a finite volume unstructured CFD code. The parallelization of the solver is based on the domain decomposition approach using the single program multiple data paradigm. The Message passing interface Library (MPI) is used for communication of data. An ILU(0) iterative solver is used for smoothing the errors arising within each partition at the different grid levels, and a multi-level synchronization across the computational domain partitions is enforced in order to improve the performance of the parallelized Multigrid solver. Two synchronization strategies are evaluated: in the first the synchronization is applied across the multigrid levels during the restriction step in addition to the base level, while in the second the synchronization is enforced during the restriction and prolongation steps. To increase robustness gathering of coefficients across partitions for the coarsest level is investigated. Tests on a number of grids from 100,00 to 800,000 elements for diffusion and advection problems have been conducted on up to 20 processors.

International Journal of Mechanical Engineering Education, 1996

This paper describes IDGG, an Interactive Dynamic Grid Generator, for use as an educational tool ... more This paper describes IDGG, an Interactive Dynamic Grid Generator, for use as an educational tool by students studying computational fluid dynamics. The package is a Windows applications and runs on IBM PC, or compatible, computers. It is written in Pascal and built using object-oriented programming. The computer program allows the user to generate boundary-fitted curvilinear grids in any two-dimensional domain. The procedure adopted requires the user to perform the transformation step by step allowing him/her to easily grasp the concept of boundary-fitted coordinate systems. In addition, IDGG may be used by CFD researchers to display results graphically in the form of vector fields, contours, and two- and three-dimensional plots. The examples provided show the effectiveness of the package as a teaching aid.

Numerical Heat Transfer, Part B: Fundamentals, 2014

The paper deals with assessing the performance of three algorithms (full multiphase, MUSIG, and H... more The paper deals with assessing the performance of three algorithms (full multiphase, MUSIG, and H-MUSIG) for the simulation of mixing and evaporation of droplets injected into a stream flowing at supersonic speeds. All algorithms, implemented within a finite volume method, use an Eulerian pressure-based formulation but differ in the representation of the disperse phase. In the full multiphase approach each

Physics of Fluids, 2008

This paper deals with the formulation, implementation, and testing of three numerical techniques ... more This paper deals with the formulation, implementation, and testing of three numerical techniques based on (i) a full multiphase approach, (ii) a MUlti-SIze Group (MUSIG) approach, and (iii) a Heterogeneous MUSIG (H-MUSIG) approach for the prediction of mixing and evaporation of liquid droplets injected into a stream of air. The numerical procedures are formulated following an Eulerian approach, within a pressure-based fully conservative Finite Volume method equally applicable in the subsonic, transonic, and supersonic regimes, for the discrete and continuous phases. The k-ε two-equation turbulence model is used to account for the droplet and gas turbulence with modifications to account for compressibility at high speeds. The performances of the various methods are compared by solving for two configurations involving stream-wise and cross-stream spraying into subsonic and supersonic streams. Results, displayed in the form of droplet velocity vectors, contour plots, and axial profiles indicate that solutions obtained by the various techniques exhibit similar behavior. Differences in values are relatively small with the largest being associated with droplet volume fractions and vapor mass fraction in the gas phase. This is attributed to the fact that with MUSIG and H-MUSIG no droplet diameter equation is solved and the diameter of the various droplet phases are held constant, as opposed to the full multiphase approach.