The development of preliminary modifications for an improved full approximation storage method in pressure-based flow solvers (original) (raw)
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Journal of Computational Physics, 2009
This paper reports on a newly developed fully coupled pressure-based algorithm for the solution of laminar incompressible flow problems on collocated unstructured grids. The implicit pressure-velocity coupling is accomplished by deriving a pressure equation in a procedure similar to a segregated SIMPLE algorithm using the Rhie-Chow interpolation technique and assembling the coefficients of the momentum and continuity equations into one diagonally dominant matrix. The extended systems of continuity and momentum equations are solved simultaneously and their convergence is accelerated by using an algebraic multigrid solver. The performance of the coupled approach as compared to the segregated approach, exemplified by SIMPLE, is tested by solving five laminar flow problems using both methodologies and comparing their computational costs. Results indicate that the number of iterations needed by the coupled solver for the solution to converge to a desired level on both structured and unstructured meshes is grid independent. For relatively coarse meshes, the CPU time required by the coupled solver on structured grid is lower than the CPU time required on unstructured grid. On dense meshes however, this is no longer true. For low and moderate values of the grid aspect ratio, the number of iterations required by the coupled solver remains unchanged, while the computational cost slightly increases. For structured and unstructured grid systems, the required number of iterations is almost independent of the grid size at any value of the grid expansion ratio. Recorded CPU time values show that the coupled approach substantially reduces the computational cost as compared to the segregated approach with the reduction rate increasing as the grid size increases.
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2010
In this study, a new cell agglomeration technique is developed and applied to 1 st and 2 nd order inviscid/viscous multigrid flow solutions on unstructured/hybrid grids. The grid coarsening required by the multigrid scheme is achieved by agglomerating the unstructured/hybrid cells based on their distribution on a quadtree data structure. The paper presents the coarsening strategy and the multigrid adaptation on inviscid/viscous 2D solutions over a NACA 0012 airfoil section. It is shown that, the quadtree based agglomeration and grid coarsening provides well defined, nested, body fitted coarse grid with optimum aspect ratio cells at all coarse grid levels. In the cases studies, it is observed that, the multigrid flow solutions obtained in this study provide convergence accelerations about 5 to 36 times for low speed inviscid flows and in a range of 3.5 to 71 fold for viscous flows.
A Coupled Incompressible Flow Solver on Structured Grids
Numerical Heat Transfer, Part B: Fundamentals, 2007
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A local grid refinement technique based upon Richardson extrapolation
Applied Mathematical Modelling, 1997
A grid-embedding technique for the solution of two-dimensional incompressible flows gouemed by the Nauier-Stokes equations is presented. A single coarse grid covers the whole domain, and local grid refinement is carried out in the resions of high gradients without changing the basic grid structure. A finite volume method with collocated primitive variables is employed, ensuring conservation at the interfaces of embedded grids, as well as global conservation. The method is applied to the simulation of a turbulent flow past a backward facing step, the flow over a square obstacle, and the flow in a sudden pipe expansion, and the predictions are compared with data published in the literature. They show that neither the convergence rate nor the stability of the method are affected by the presence of embedded grids. The grid-embedding technique yields significant savings in computing time to achieve the same accuracy obtained using conventional grids.
A finite point method for adaptive three-dimensional compressible flow calculations
International Journal for Numerical Methods in Fluids, 2009
The finite point method (FPM) is a meshless technique, which is based on both, a weighted least-squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind-biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h-adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution-based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented. resources and ever-challenging demands for practical and theoretical applications. Nowadays, there are two main types of numerical techniques for solving PDEs. On the one hand, there exist meshbased or conventional discretization methods; among them the classical finite differences (FD), finite volume (FV) and finite element (FE) methods are of singular interest. These techniques are mostly employed in practice due to their robustness, efficiency and high confidence gained through years of continuous use and enhancement. On the other hand, there exist meshless methods. Having their pros and cons, meshless methods offer an alternative to mesh-based techniques. Meshless methods are conceptually attractive; however, their practical implementations have not succeeded so far to prove their efficiency and this is a fact which can explain the comparatively little attention that has been devoted to these techniques. In spite of this, over the last 10 years, some difficulties that arose in conventional mesh-based methods when performing particular applications have brought meshless methods into the focus of attention.
Numerical flow modelling in a locally refined grid
International Journal for Numerical Methods in Engineering, 1994
An algorithm is presented to model two-dimensional, non-isothermal, low Mach number flows with a local steep density gradient. The algorithm uses an adaptive, locally refined, non-staggered grid and has been developed, especially for modelling laminar flames. The governing equations, based on a stream-function-vorticity formulation, are presented and discretized using hybrid finite differences. A (isothermal) tcst problem is presented to compare the accuracy of the results of the solver presented in this paper, with the results of algorithms found in the literature. However, this test problem proves to be not well suited for the application of a locally refined grid, since it does not contain a local steep gradient. For this reason an additional test problem is constructed that clearly shows the advantages of the locally refined grid as compared to a uniform grid with respect to both the calculation time as well as the number of grid nodes needed. Furthermore, a laminar premixed flame is modelled with simple chemistry to show that the algorithm, presented in this paper, converges to a stabilized flame when an adaptive grid technique is used.
A pressure-based framework for the resolution of multi-fluid flow problems
2013
In this paper, the class of segregated single-fluid all speed flow algorithms is extended to multi-fluid flow simulations using a unified, compact, and easy to understand notation. Depending on the constraint equation used to derive the pressure (or pressure correction) equation, the extended algorithms are shown to fall under two categories denoted in this work by the geometric conservation based algorithms and the mass conservation based algorithms, respectively. The differences and similarities between the two categories are explained. Several techniques developed to promote and accelerate the convergence of these algorithms are also presented. P refers to the P grid point. Superscripts C refers to convection contribution. D refers to diffusion contribution. (k) refers to fluid/phase k. ,.. refers to first, second, … updated value at the current iteration. refers to values of fluid/phase k from the previous iteration. refers to correction field of phase/fluid k. old refers to values from the previous time step. sx refers to SIMPLEX. x,y,z refers to components in x, y, and z directions. µ (k) (k)*,(k)** (k) !
A pressure-based unstructured grid method for all-speed flows
International Journal for Numerical Methods in Fluids, 2000
An all-speed algorithm based on the SIMPLE pressure-correction scheme and the 'retarded-density' approach has been formulated and implemented within an unstructured grid, finite volume (FV) scheme for both incompressible and compressible flows, the latter involving interaction of shock waves. The collocated storage arrangement for all variables is adopted, and the checkerboard oscillations are eliminated by using a pressure-weighted interpolation method, similar to that of Rhie and Chow [Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal 1983; 21: 1525]. The solution accuracy is greatly enhanced when a higher-order convection scheme combined with adaptive mesh refinement (AMR) are used.
Adaptive Grid Refinement in Incompressible Flow by
The overall objective of the present research work is to solve the physical problem related to fluid dynamics of incompresible isotropic type of fluids , what happens in any industry they have big plants in which they perform wind tunnel testing and so many which are obiviously so much coastly and time consuming. Many great Scientists and various researh scholars have already contributed so much in relating variation of such physical variation of fluids with Mathematics. Thus the concept of "Computational Fluid Dynamics" motivated us to work in this field, during the period of six month of our B.tech Project we have learned many interesting algorithms and several fundamental properties of various kinds of fluid flow , we developed our flexible computational programmes which can solve Navier Stokes Equation for incompressible flows accompanied with different boundary conditions across any finite control volume. We have adopted the concept of SIMPLE-Method given by Patnakar[3] for collocated grid although the SIMPLE-staggered grid method enjoyed considerable success particularly when Cartesian grids were employed, but the procedure was found to be inconvenient when curvilinear or adaptive grids were to be employed to compute over more complex domains. It was found that if the pressure correction equation as derived for staggered grids was used to predict pressure on collocated grids the resulting pressure distribution showed zig-zagness. Here we shall describe the method proposed by A.W Date [1]that elegantly eliminates the problem of zigzag pressure prediction. Later we have discussed about the Advance topic in CFD "The Concept of Adaptive Grid" , the beauty of adaptive grid is that it adjust physical plane in such a way so that it represent the dynamic variation occurring because of gradient of some physical quantities on Cartesian plane, for obtaining these values in curvilinear coordinate system we have to solve Navier-Stokes equations of mass, momentum and energy for compressible and viscous fluid.
Numerical Heat Transfer, Part B: Fundamentals, 2004
This paper deals with the evaluation of six segregated high-resolution pressure-based algorithms, which extend the SIMPLE, SIMPLEC, PISO, SIMPLEX, SIMPLEST, and PRIME algorithms, originally developed for incompressible flow, into compressible flow simulations. The algorithms are implemented within a single grid, a prolongation grid, and a full multigrid method and their performance assessed by solving problems in the subsonic, transonic, supersonic, and hypersonic regimes. This study clearly demonstrates that all algorithms are capable of predicting fluid flow at all speeds and qualify as efficient smoothers in multigrid calculations. In terms of CPU efficiency, there is no global and consistent superiority of any algorithm over the others, even though PRIME and SIMPLEST are generally the most expensive for inviscid flow problems. Moreover, these two algorithms are found to be very unstable in most of the cases tested requiring considerable upwind bleeding (up to 50%) of the high resolution scheme to promote convergence. The most stable algorithms are SIMPLEC and SIMPLEX. Moreover, the reduction in computational effort associated with the prolongation grid method reveals the importance of initial guess in segregated solvers. The most efficient method is found to be the full multigrid method, which resulted in a convergence acceleration ratio, in comparison with the single grid method, as high as 18.4.