An improved low diffusion E-CUSP upwind scheme

Zha, Gecheng; Shen, Yiqing; Wang, Baoyuan

doi:10.1016/j.compfluid.2011.03.012

Cited by 135 publications

(49 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…The preconditioning methodology of this paper is based on the recent E-CUSP scheme suggested by Zha et al [17]. In [13,14,16,17], the characteristic analysis is given as the foundation to construct the E-CUSP scheme.…”

Section: Preconditioning Of the Low Diffusion E-cusp (Lde) Schemementioning

confidence: 99%

“…The different formulations for U + , U À , P + and P À can be found in [13,14,16,17] with different behavior. The preconditioning of the LDE scheme needs to satisfy two conditions when the flow velocity approaching zero: (1) the eigenvalues of the Jacobian matrices should be at the same order of magnitude of the velocity and (2) the numerical dissipation should diminish.…”

Section: Preconditioning Of the Low Diffusion E-cusp (Lde) Schemementioning

confidence: 99%

“…In [13,14,16,17], the characteristic analysis is given as the foundation to construct the E-CUSP scheme. The basic idea is to split the flux E to the convective flux E c and the pressure flux E p .…”

Section: Preconditioning Of the Low Diffusion E-cusp (Lde) Schemementioning

confidence: 99%

“…The Liou's AUSM family schemes [4][5][6][7][8][9], van Leer-Hänel scheme [10], and Edwards's LDFSS schemes [11,12] belong to the H-CUSP group. The schemes developed by Zha et al [13][14][15][16][17] belong to the E-CUSP group.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

Shen

Zha

2012

Computers & Fluids

Self Cite

View full text Add to dashboard Cite

a b s t r a c tA low diffusion E-CUSP (LDE) scheme for preconditioned Navier-Stokes equations is developed. The LDE scheme with high-order WENO reconstruction and high order difference scheme for viscous terms is used to simulate several flows at various speed from low speed natural convection to supersonic flows. The unfactored implicit Gauss-Seidel relaxation scheme, in which the preconditioned Roe's matrices are used, is used for time integration. Numerical results are presented to show efficiency, accuracy and robustness of the new preconditioning scheme.

show abstract

An unsteady preconditioning scheme based on convective‐upwind split‐pressure artificial dissipation

Folkner

Katz

Sankaran

2015

Numerical Methods in Fluids

View full text Add to dashboard Cite

SummaryObtaining accurate computational results for low‐Mach‐number unsteady flows presents significant challenges for numerical schemes. In this work, we present a novel preconditioning scheme designed to provide good conditioning for these flows at all Strouhal numbers. The approach is based on the convective‐upwind split‐pressure scheme, which naturally facilitates the proper scaling of velocity and pressure dissipation terms for low‐Mach‐number unsteady flows. Unlike traditional matrix dissipation schemes, the preconditioned convective‐upwind split‐pressure scheme formulation provides scalar‐like efficiency and simplicity. Several test cases are presented for steady, unsteady, convection‐dominated, and acoustic‐dominated flows that demonstrate significant improvements in accuracy and convergence rate over traditional preconditioning schemes for a wide range of flow conditions. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

An improved low diffusion E-CUSP upwind scheme

Cited by 135 publications

References 25 publications

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

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

Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

An unsteady preconditioning scheme based on convective‐upwind split‐pressure artificial dissipation

Contact Info

Product

Resources

About