Efficient unsteady high Reynolds number flow computations on unstructured grids

Lucas, Peter; Bijl, H.; Zuijlen, A.H. van

doi:10.1016/j.compfluid.2009.09.004

Cited by 12 publications

(23 citation statements)

References 41 publications

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“…Both ESDIRK and Rosenbrock methods, when incorporated with suitable adaptive time stepping, are widely studied in computational fluid dynamics, especially in solving stiff problems that admit a variety of time scales; see, e.g. [19,28] for further references.…”

Section: Fully Implicit Adaptive Time Steppingmentioning

confidence: 99%

A Scalable Fully Implicit Compressible Euler Solver for Mesoscale Nonhydrostatic Simulation of Atmospheric Flows

Yang¹,

Cai²

2014

SIAM J. Sci. Comput.

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Abstract. A fully implicit solver is developed for the mesoscale nonhydrostatic simulation of atmospheric flows governed by the compressible Euler equations. To spatially discretize the Euler equations on a height-based terrain-following mesh, we apply a cell-centered finite volume scheme, in which an AUSM + -up method with a piecewise linear reconstruction is employed to achieve secondorder accuracy for the low-Mach flow. A second-order ESDIRK method with adaptive time stepping is applied to stabilize physically insignificant fast waves and accurately integrate the Euler equations in time. The nonlinear system arising at each time step is solved by using a Jacobian-free NewtonKrylov-Schwarz algorithm. To accelerate the convergence and improve the robustness, we employ a class of additive Schwarz preconditioners in which the subdomain Jacobian matrix is constructed using a first-order spatial discretization. Several test cases are used to validate the correctness of the scheme and examine the performance of the solver. Large-scale results on a supercomputer with up to 18, 432 processor cores are provided to show the parallel performance of the proposed method.

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Section: Fully Implicit Adaptive Time Steppingmentioning

confidence: 99%

A Scalable Fully Implicit Compressible Euler Solver for Mesoscale Nonhydrostatic Simulation of Atmospheric Flows

Yang¹,

Cai²

2014

SIAM J. Sci. Comput.

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“…On the other hand, it is considerably sparser than that obtained using more traditional FV discretizations, which typically extend up to distance-2 [1] or even distance-3 neighbors [8]. In these latter cases, contributions from the outermost gridpoints in the stencil have to be neglected [1], or at least lumped [8], when constructing the Jacobian approximation upon which the ILU(ℓ) preconditioner is built. These approximations are a potential source of performance degradation as reported in [8].…”

Section: Fully Coupled Solution Strategy With Fd Newton Linearizationmentioning

confidence: 98%

“…Blocking the flow variables in this way, also referred to as "field interlacing" in the literature, is acknowledged [7][8][9] to result in better performances than grouping variables per aerodynamic quantity.…”

Section: Space Discretisationmentioning

confidence: 99%

“…In these latter cases, contributions from the outermost gridpoints in the stencil have to be neglected [1], or at least lumped [8], when constructing the Jacobian approximation upon which the ILU(ℓ) preconditioner is built. These approximations are a potential source of performance degradation as reported in [8]. The memory occupation required to store the Jacobian matrix still remains remarkable.…”

Section: Fully Coupled Solution Strategy With Fd Newton Linearizationmentioning

confidence: 99%

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Multilevel Variable-Block Schur-Complement-Based Preconditioning for the Implicit Solution of the Reynolds- Averaged Navier-Stokes Equations Using Unstructured Grids

Carpentieri¹,

Bonfiglioli²

2018

Computational Fluid Dynamics - Basic Instruments and Applications in Science

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Implicit methods based on the Newton's rootfinding algorithm are receiving an increasing attention for the solution of complex Computational Fluid Dynamics (CFD) applications due to their potential to converge in a very small number of iterations. This approach requires fast convergence acceleration techniques in order to compete with other conventional solvers, such as those based on artificial dissipation or upwind schemes, in terms of CPU time. In this chapter, we describe a multilevel variable-block Schur-complement-based preconditioning for the implicit solution of the Reynoldsaveraged Navier-Stokes equations using unstructured grids on distributed-memory parallel computers. The proposed solver detects automatically exact or approximate dense structures in the linear system arising from the discretization, and exploits this information to enhance the robustness and improve the scalability of the block factorization. A complete study of the numerical and parallel performance of the solver is presented for the analysis of turbulent Navier-Stokes equations on a suite of threedimensional test cases.

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“…Both, however, become impractical for three dimensional computations on unstructured grids. In order to address this problem, recently, Lucas et al [49] proposed a Newton linearization in combination with a Krylov subspace technique for unsteady flow computations. To maintain the locality of the discontinuous Galerkin discretization, we prefer however the use of pseudotime integration methods using explicit Runge-Kutta time integrators.…”

Section: Figure 12: When Water Flow Enters a Contraction At A Certaimentioning

confidence: 99%

Discontinuous Galerkin finite element methods for (non)conservative partial differential equations

Rhebergen¹

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Efficient unsteady high Reynolds number flow computations on unstructured grids

Cited by 12 publications

References 41 publications

A Scalable Fully Implicit Compressible Euler Solver for Mesoscale Nonhydrostatic Simulation of Atmospheric Flows

A Scalable Fully Implicit Compressible Euler Solver for Mesoscale Nonhydrostatic Simulation of Atmospheric Flows

Multilevel Variable-Block Schur-Complement-Based Preconditioning for the Implicit Solution of the Reynolds- Averaged Navier-Stokes Equations Using Unstructured Grids

Discontinuous Galerkin finite element methods for (non)conservative partial differential equations

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