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

Shen, Yiqing; Zha, Gecheng

doi:10.1016/j.compfluid.2011.10.013

Cited by 8 publications

(9 citation statements)

References 57 publications

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“…The scheme we tested here may not be an optimal one. In order to reduce a systematic error due to biased selection of WENO schemes, we also tried the WENO methods in [8,19]. The WENO-SW solutions presented in the current paper are more accurate than those WENO solutions in the literature.…”

Section: Cavity Flowmentioning

confidence: 77%

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Comparison of Fifth-Order WENO Scheme and Finite Volume WENO-Gas-Kinetic Scheme for Inviscid and Viscous Flow Simulation

Luo

Xuan

2013

Commun. comput. phys.

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The development of high-order schemes has been mostly concentrated on the limiters and high-order reconstruction techniques. In this paper, the effect of the flux functions on the performance of high-order schemes will be studied. Based on the same WENO reconstruction, two schemes with different flux functions, i.e., the fifthorder WENO method and the WENO-Gas-kinetic scheme (WENO-GKS), will be compared. The fifth-order finite difference WENO-SW scheme is a characteristic variable reconstruction based method which uses the Steger-Warming flux splitting for inviscid terms, the sixth-order central difference for viscous terms, and three stages Runge-Kutta time stepping for the time integration. On the other hand, the finite volume WENO-GKS is a conservative variable reconstruction based method with the same WENO reconstruction. But, it evaluates a time dependent gas distribution function along a cell interface, and updates the flow variables inside each control volume by integrating the flux function along the boundary of the control volume in both space and time. In order to validate the robustness and accuracy of the schemes, both methods are tested under a wide range of flow conditions: vortex propagation, Mach 3 step problem, and the cavity flow at Reynolds number 3200. Our study shows that both WENO-SW and WENO-GKS yield quantitatively similar results and agree with each other very well provided a sufficient grid resolution is used. With the reduction of mesh points, the WENO-GKS behaves to have less numerical dissipation and present more accurate solutions than those from the WENO-SW in all test cases. For the Navier-Stokes equations, since the WENO-GKS couples inviscid and viscous terms in a single flux evaluation, and the WENO-SW uses an operator splitting technique, it appears that the WENO-SW is more sensitive to the WENO reconstruction and boundary treatment. In terms of efficiency, the finite volume WENO-GKS is about 4 times slower than the finite difference WENO-SW in two dimensional simulations. The current study clearly shows that besides high-order reconstruction, an accurate gas evolution model or flux function in a high-order scheme is also important in the capturing of * Corresponding author. Email addresses: luojun@ust.hk (J. Luo), maljxuan@ust.hk (L. Xuan), makxu@ust.hk (K. Xu) http://www.global-sci.com/ 599 c 2013 Global-Science Press 600 J. Luo, L. Xuan and K. Xu / Commun. Comput. Phys., 14 (2013), pp. 599-620physical solutions. In a physical flow, the transport, stress deformation, heat conduction, and viscous heating are all coupled in a single gas evolution process. Therefore, it is preferred to develop such a scheme with multi-dimensionality, and unified treatment of inviscid and dissipative terms. A high-order scheme does prefer a high-order gas evolution model. Even with the rapid advances of high-order reconstruction techniques, the first-order dynamics of the Riemann solution becomes the bottleneck for the further development of high-order schemes. In order to avoid the weakness of th...

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Section: Cavity Flowmentioning

confidence: 77%

“…The WENO-SW solutions presented in the current paper are more accurate than those WENO solutions in the literature. In [8,19], the cavity solutions from other WENO schemes are presented.…”

Section: Cavity Flowmentioning

confidence: 99%

Comparison of Fifth-Order WENO Scheme and Finite Volume WENO-Gas-Kinetic Scheme for Inviscid and Viscous Flow Simulation

Luo

Xuan

2013

Commun. comput. phys.

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“…Similarly, Zha et al . provides a modification to CUSP suitable for low‐Mach‐number steady flows, although it appears that this formulation more closely resembles the AUSM framework.…”

Section: Introductionmentioning

confidence: 99%

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

Folkner

Katz

Sankaran

2015

Numerical Methods in Fluids

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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.

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“…For the steady case, Liou provides a modification to extend AUSM for all speeds, which he terms AUSM + -up [11]. Similarly, Zha et al [14,15] provides a modification to CUSP suitable for low Mach number steady flows, although it appears that this formulation more closely resembles the AUSM framework.…”

Section: Introductionmentioning

confidence: 94%

“…To solve the issue in AUSM, Liou introduced two new forms of dissipation into the AUSM scheme: additional pressure dissipation for the interfacial Mach number and additional velocity diffusion to the pressure terms. While the addition of pressure dissipation has been used extensively in the literature [14,15,8] with much success, the effects of velocity dissipation are less clear. Since the focus is on low speed flows, velocity dissipation is omitted.…”

Section: Preconditioned Cusp Schemementioning

confidence: 99%

An Unsteady Preconditioning Scheme Based on Convective-Upwind Split-Pressure (CUSP) Artificial Dissipation

Katz

Folkner

Sankaran

2014

52nd Aerospace Sciences Meeting

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

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

Cited by 8 publications

References 57 publications

Comparison of Fifth-Order WENO Scheme and Finite Volume WENO-Gas-Kinetic Scheme for Inviscid and Viscous Flow Simulation

Comparison of Fifth-Order WENO Scheme and Finite Volume WENO-Gas-Kinetic Scheme for Inviscid and Viscous Flow Simulation

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

An Unsteady Preconditioning Scheme Based on Convective-Upwind Split-Pressure (CUSP) Artificial Dissipation

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