On the accuracy of upwind schemes for the solution of the Navier-Stokes equations

Haenel, D.; Schwane, Richard; Seider, Gerald

doi:10.2514/6.1987-1105

Cited by 88 publications

(64 citation statements)

References 2 publications

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“…In [25], the basic method can be either AUSMDV (a blend of AUSMD and AUSMV) or FDSROE. The partner dissipative schemes used in the switching are respectively FVS (Hänel version [7]) and HLL. Even in this case, the cure is very efficient, as we have also experimented in our numerical exercises by matching the basic method FDSPAN and the dissipative FVSVL one.…”

Section: Cures For the Carbunclementioning

confidence: 99%

Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon

Pandolfi¹,

D’Ambrosio²

2001

Journal of Computational Physics

289

215

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Section: Cures For the Carbunclementioning

confidence: 99%

Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon

Pandolfi¹,

D’Ambrosio²

2001

Journal of Computational Physics

289

215

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“…The H-CUSP schemes have the total enthalpy from the energy equation in their convective vector, whereas the E-CUSP schemes use the total energy in the convective vector. The Liou's AUSM family schemes [24][25][26][27][28], Van Leer-Hänel scheme [29], and Edwards's LDFSS schemes [30,31] belong to the H-CUSP group. The schemes developed by Zha et al [32][33][34][35][36] belong to the E-CUSP group.…”

Section: Introductionmentioning

confidence: 99%

E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

Shen

Zha

Huerta

2012

Journal of Computational Physics

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a b s t r a c tAn E-CUSP (energy-convective upwind and split pressure) scheme is developed to solve the equations of magnetohydrodynamics. Fifth order WENO reconstructions are employed to calculate the fluxes in order to achieve high order spacial accuracy. A characteristic speed of sound by averaging the fast wave speed and the acoustic speed of sound is suggested to evaluate the Mach number, which will yield robust and accurate solutions. The numerical experiments have demonstrated the accuracy and the capability of the new scheme to capture complex interactions of multiple shocks and vortices.

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“…The inviscid F c and viscous F v parts of the numerical flux are treated independently. For the former, exact Riemann flux, approximate Roe flux-difference splitting or the approximate Van Leer flux-difference splitting as modified by Hänel [9] were used, while for the viscous flux discretization we adopted the BR2 scheme presented in [10,11] and theoretically analyzed in [8,12] (where it is referred to as BRMPS). The numerical viscous flux is given by:…”

Section: Dg Approximation Of the Navier-stokes Equationsmentioning

confidence: 99%

Hybrid Openmp/Mpi Parallelization of a High–order Discontinuous Galerkin CFD Solver

Bassi¹,

Colombo²,

Crivellini³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. This paper describes the implementation of an hybrid OpenMP/MPI parallelization strategy in a Discontinuous Galerkin solver used for DNS and LES or CAA computations, to fruitfully exploit the modern massively parallel HPC facilities. It is usually believed that the sheared memory view of OpenMP can easily increase the parallel efficiency of codes dealing with multi-core clusters. The idea consists of running calculations on those machines restricting as much as possible the use of the MPI library to the communications between nodes and exploiting the shared memory paradigm within a node. However, in practice, the achievement of a real parallel performance gain is not straightforward. Moreover, as far as DG solvers are concerned, almost nothing is reported in the current literature about the hybrid MPI/OpenMP implementation. In this work a colouring algorithm has been employed for OpenMP. The resulting hybrid strategy performs quite satisfactory, since generally it is more efficient of the pure MPI implementation. However, the performances are heavily dependent on hardware platforms, as well as on computational details such as the polynomial order of space discretization or the number of computational elements. Several scalability tests have been performed, resulting in the conclusion that the best performance can be achieved only with a proper choice of the number of MPI partition and OpenMP threads to be used within a single node. The reliability of the method was here assessed by solving the Taylor Green vortex problem at Reynolds numbers equal to 800 and 1600 and the Linear Euler acustic scattering from a rigid sphere.

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On the accuracy of upwind schemes for the solution of the Navier-Stokes equations

Cited by 88 publications

References 2 publications

Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon

Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon

E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

Hybrid Openmp/Mpi Parallelization of a High–order Discontinuous Galerkin CFD Solver

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