Fast Solvers for Unsteady Thermal Fluid Structure Interaction (original) (raw)
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Fast Solvers for Thermal Fluid Structure Interaction
We consider thermal fluid structure interaction to model industrial gas quenching in steel forging, where hot steel is cooled using cold high pressured gas. This allows to define properties of the finished steel part, as for example yield strength, locally at low cost and without environmental problems. For the numerical simulation, a partitioned approach via a Dirichlet-Neumann coupling and a fixed point iteration is employed. In time, previously developed efficient time adaptive higher order time integration schemes are used. The respective models are the compressible Navier-Stokes equations and the nonlinear heat equation, where the parameter functions are obtained from measurements on a specific steel. Here, the use of different vector extrapolation methods for convergence acceleration techniques of the fixed point iteration is analyzed. In particular, Aitken relaxation, minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are considered.
Extrapolation in Time in Thermal Fluid Structure Interaction
Lecture Notes in Computational Science and Engineering, 2015
We consider time dependent thermal fluid structure interaction. The respective models are the compressible Navier-Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet-Neumann method and a fixed point iteration is employed. As a reference solver a previously developed efficient time adaptive higher order time integration scheme is used. To improve upon this, we work on reducing the number of fixed point coupling iterations. Thus, we explore the idea of extrapolation based on data given from the time integration and derive such methods for SDIRK2. This allows to reduce the number of fixed point iterations further by up to a factor of two with linear extrapolation performing better than quadratic.
A time-adaptive fluid-structure interaction method for thermal coupling
2010
The thermal coupling of a fluid and a structure is of great significance for many industrial processes. As a model for cooling processes in heat treatment of steel we consider the surface coupling of the compressible Navier-Stokes equations bordering at one part of the surface with the heat equation in a solid region. The semi-discrete coupled system is solved using stiffly stable SDIRK methods of higher order, where on each stage a fluid-structurecoupling problem is solved. For the resulting method it is shown by numerical experiments that a second order convergence rate is obtained. This property is further used to implement a simple time-step control, which saves considerable computational time and, at the same time, guarantees a specified maximum error of time integration.
Combined interface boundary condition method for unsteady fluid–structure interaction
A new procedure for modeling the conjugate heat-transfer process between fluid and structure subdomains is presented. The procedure relies on higher-order combined interface boundary conditions (CIBC) for improved accuracy and stability. Traditionally, continuity of temperature and heat flux along interfaces is satisfied through algebraic jump conditions in a staggered fashion. More specifically, Dirichlet temperature conditions are usually imposed on the fluid side and Neumann heat-flux conditions are imposed on the solid side for the stability of conventional sequential staggered procedure. In this type of treatment, the interface introduces additional stability constraints to the coupled thermal simulations. By utilizing the CIBC technique on the Dirichlet boundary conditions, a staggered procedure can be constructed with the same order of accuracy and stability as those of standalone computations. Using the Godunov-Ryabenkii normal-mode analysis, a range of values of the coupling parameter is found that yields a stable and accurate interface discretization. The effectiveness of the method is investigated by presenting and discussing performance evaluation data using a 1D finite-difference formulation for each subdomain. and cooling of turbine blades in jet engines , and thermoelastic deformation of a structure due to aerodynamic heating . One way of modeling the above phenomena is to use a monolithic (i.e. tightly coupled) discretization for both solid and fluid subdomains with the interface boundary conditions . However, one generally solves different equations in the solid and fluid subdomains: Typically, the unsteady thermal diffusion equation is computed in the solid subdomain, and the Navier-Stokes equations supplemented by appropriate turbulence models are solved in the fluids subdomain. In addition, the discretization approaches are often different: Commonly, the finite-element method is used in the solid subdomain, whereas the finite-volume method is adopted in the fluid subdomain. These differences can lead to difficulties in developing a computationally efficient monolithic scheme.
Adaptive time stepping for fluid-structure interaction solvers
Finite Elements in Analysis and Design
A novel adaptive time stepping scheme for fluid-structure interaction (FSI) problems is proposed that allows for controlling the accuracy of the time-discrete solution. Furthermore, it eases practical computations by providing an efficient and very robust time step size selection. This has proven to be very useful, especially when addressing new physical problems, where no educated guess for an appropriate time step size is available. The fluid and the structure field, but also the fluid-structure interface are taken into account for the purpose of a posteriori error estimation, rendering it easy to implement and only adding negligible additional cost. The adaptive time stepping scheme is incorporated into a monolithic solution framework, but can straightforwardly be applied to partitioned solvers as well. The basic idea can be extended to the coupling of an arbitrary number of physical models. Accuracy and efficiency of the proposed method are studied in a variety of numerical examples ranging from academic benchmark tests to complex biomedical applications like the pulsatile blood flow through an abdominal aortic aneurysm. The demonstrated accuracy of the time-discrete solution in combination with reduced computational cost make this algorithm very appealing in all kinds of FSI applications.
Partitioned solver for strongly coupled fluid–structure interaction
Computers & Fluids, 2013
In this work a fluid-structure interaction solver is developed in a partitioned approach using block Gauss-Seidel implicit scheme. Finite volume method is used to discretize the fluid flow problem on a moving mesh in an arbitrary Lagrangian-Eulerian formulation and by using an adaptive time step. The pressure-velocity coupling is performed by using the PIMPLE algorithm, a combination of both SIMPLE and PISO algorithms, which permits the use of larger time steps in a moving mesh. The structural elastic deformation is analyzed in a Lagrangian formulation using the St. Venant-Kirchhoff constitutive law, for non-linear large deformations. The solid structure is discretized by the finite volume method in an iterative segregated approach. The automatic mesh motion solver is based on Laplace smoothing equation with variable mesh diffusion. The strong coupling between the different solvers and the equilibrium on the fluid-structure interface are achieved by using an iterative implicit fixed-point algorithm with dynamic Aitken's relaxation method. The solver, which is called vorflexFoam, is developed using the open source C++ library OpenFOAM. The solver is validated on two different benchmarks largely used in the open literature. In the first one the structural deformation is induced by incompressibility. The second benchmark consists on a vortex excited elastic flap in a Von Karman vortex street. Finally, a more complex case is studied including two elastic flaps immersed in a pulsatile flow. The present solver detects accurately the interaction between the complex flow structures generated by the flaps and the effect of the flaps oscillations between each other.
An algorithm for the simulation of thermally coupled low speed flow problems
SUMMARY In this paper, we propose a computational algorithm for the solution of thermally coupled flows in subsonic regime. The formulation is based upon the compressible Navier–Stokes equations, written in nonconserva-tion form. An efficient modular implementation is obtained by solving the energy equation separately and then using the computed temperature as a known value in the momentum-continuity system. If an explicit single-step time integration scheme for the energy equation is used, the decoupling results to be natural. Integration of the momentum-continuity system is carried out using a semi-explicit method, combining Runge–Kutta and Backward Euler schemes for the momentum and continuity equations, respectively. Implicit treatment of pressure leads to favorable time step estimates even in the low Mach number (Ma 1) regimes. The numerical dissipation introduced by the Backward Euler scheme ensures absence of the spurious high frequencies in the numerical solution. The key point of the method is the assumption of linear variation of the temperature within a time step. Combined with a fractional splitting of the momentum-continuity system, it allows to solve the continuity only once per time step. Omitting the necessity of solving for the pressure at every intermediate step of the Runge–Kutta scheme minimizes the computational cost associated to the implicit step and leads to an efficiency close to that of a purely explicit scheme. The method is tested using two benchmark examples.
Fixed point fluid structure interaction solvers with dynamic relaxation
A fixed-point fluid-structure interaction (FSI) solver with dynamic relaxation is revisited. New developments and insights gained in recent years motivated us to present an FSI solver with simplicity and robustness in a wide range of applications. Particular emphasis is placed on the calculation of the relaxation parameter by both Aitken's ∆ 2 method and the method of steepest descent. These methods have shown to be crucial ingredients for efficient FSI simulations.
Stable and accurate loosely-coupled scheme for unsteady fluid-structure interaction
AIAA Paper, 2007
This paper presents a new loosely-coupled partitioned procedure for modeling fluid-structure interaction. The procedure relies on a higher-order Combined Interface Boundary Condition (CIBC) treatment for improved accuracy and stability of fluid-structure coupling. Traditionally, continuity of velocity and momentum flux along interfaces are satisfied through algebraic interface conditions applied in a sequential fashion, which is often referred to staggered computation. In existing staggered procedures, the interface conditions undermine stability and accuracy of coupled fluid-structure simulations. By utilizing the CIBC technique on the velocity and momentum flux boundary conditions, a staggered coupling procedure can be constructed with similar order of accuracy and stability of standalone computations. Introduced correction terms for velocity and momentum flux transfer can be explicitly added to the standard staggered time-stepping stencils so that the discretization is well-defined across the deformable interface. The new formulation involves a coupling parameter, which has an interval of well-performing values for both classical 1D closed-and open-elastic piston problems. The technique is also demonstrated in 2D in conjunction with the common refinement method for subsonic flow over a thin-shell structure.
International Journal of Thermal Sciences, 2017
Partitioned approaches for the simulation of coupled conjugate heat transfer are gaining popularity in fields that require accurate thermal predictions. Considerable efforts have been put into determining stable coupling schemes, but performance enhancements have been neglected. This paper presents, for the first time, a detailed and comprehensive study of the numerical properties of Dirichlet-Robin coupling procedures, used in conjugate heat transfer simulation, with emphasis put on the optimal local coupling formulation that was recently derived from a stability analysis. This all-new optimal coupling approach provides local adaptability and has never been tested on a complex setup. This investigation looks to determine the relevance and the limitations of the theory when applied to complex conjugate heat transfer setups. The stability theory of the optimal Dirichlet-Robin coupling scheme is first recalled, then, a realistic 3D application, with complex geometry and flow structures, is used to evaluate the performance and sensitivity of Dirichlet-Robin couplings, with respect to various numerical parameters. This detailed study allows, for the first time, to evaluate the advantages and limitations of the recently proposed optimal procedure, when used on realistic 3D CHT problems. It turns out that the local optimal Dirichlet-Robin formulation outperforms all what is found in literature, and insures unconditional stability with monotone convergence for all considered setups of the 3D model.