The weighted ENO scheme based on the modified smoothness indicator

Hu, Fuxing

doi:10.1016/j.compfluid.2017.03.025

Cited by 9 publications

(9 citation statements)

References 18 publications

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“…where the second-order smoothness indicators β k , k = 0, 1, 2, derived by Hu [32] are adopted to measure the smoothness of f on the sub-stencils S k and are defined as…”

Section: Wcns Methodsmentioning

confidence: 99%

See 1 more Smart Citation

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

Jiang

Chen

Zhang

et al. 2020

Preprint

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The computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regime. This paper designs a high order semi-implicit weighted compact nonlinear scheme (WCNS) for the all-Mach isentropic Euler system of compressible gas dynamics. To avoid severe CFL restrictions for low Mach flows, the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components. A third-order implicit-explicit (IMEX) method is used for the time discretization and a fifth-order WCNS is used for the spatial discretization. The designed semi-implicit WCNS is asymptotic preserving and asymptotically accurate in the zero Mach number limit. One- and two-dimensional numerical examples in both compressible and incompressible regimes are given to demonstrate the advantages of the designed method.

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“…where the second-order smoothness indicators β k , k = 0, 1, 2, derived by Hu [32] are adopted to measure the smoothness of f on the sub-stencils S k and are defined as…”

Section: Wcns Methodsmentioning

confidence: 99%

“…Remark 2. To update the solutions from t n to t n+1 by the p th -order IMEX-ARSp WCNS, we first solve the elliptic equation (32) to obtain ρ (k) and then calculate explicitly q (k) using (35). Here, (32) is a nonlinear equation for ρ (k) , which is solved by inexact Newton-generalized minimum residual (Newton-GMRES) algorithms.…”

Section: Imex-arsp Wcnsmentioning

confidence: 99%

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

Jiang

Chen

Zhang

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…where the second-order smoothness indicators β k , k = 0, 1, 2, derived by Hu [35] are adopted to measure the smoothness of f on the sub-stencils S k .…”

Section: Wcns Methodsmentioning

confidence: 99%

“…For the GSA IMEX-ARSp scheme, ρ n+1 = ρ (s) and q n+1 = q (s) . (35) and the gradient terms in (34) and (35) are solved by the fifth-order WCNS in the component-bycomponent and dimension-by-dimension forms. Here, in the interpolation process of the cell-edge pressures, the Lax-Friedrichs flux with zero numerical viscosity is considered, i.e., p = 1 2 p + 1 2 p, otherwise the numerical diffusion will become large when ε → 0 [10].…”

Section: Imex-arsp Wcnsmentioning

confidence: 99%

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

et al. 2020

View full text Add to dashboard Cite

The computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regime. This paper designs a high order semi-implicit weighted compact nonlinear scheme (WCNS) for the all-Mach isentropic Euler system of compressible gas dynamics. To avoid severe Courant-Friedrichs-Levy (CFL) restrictions for low Mach flows, the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components. A third-order implicit-explicit (IMEX) method is used for the time discretization of the split components and a fifth-order WCNS is used for the spatial discretization of flux derivatives. The high order IMEX method is asymptotic preserving and asymptotically accurate in the zero Mach number limit. One- and two-dimensional numerical examples in both compressible and incompressible regimes are given to demonstrate the advantages of the designed IMEX WCNS.

show abstract

“…The spatial discretization of both convective terms in (33)-(35) and the gradient terms in(34) and(35)are solved by the fifth-order WCNS in the component-by-component and dimension-by-dimension forms. Here, in the interpolation process of the cell-edge pressures, the Lax-Friedrichs flux with zero numerical…”

mentioning

confidence: 99%

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

Jiang

Chen

Zhang

et al. 2020

Preprint

View full text Add to dashboard Cite

The computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regime. This paper designs a high order semi-implicit weighted compact nonlinear scheme (WCNS) for the all-Mach isentropic Euler system of compressible gas dynamics. To avoid severe Courant-Friedrichs-Levy (CFL) restrictions for low Mach flows, the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components. A third-order implicit-explicit (IMEX) method is used for the time discretization of the split components and a fifth-order WCNS is used for the spatial discretizationof flux derivatives. The high order IMEX method is asymptotic preserving and asymptotically accurate in the zero Mach number limit. One- and two-dimensional numerical examples in both compressible and incompressibleregimes are given to demonstrate the advantages of the designed IMEX WCNS.

show abstract

The weighted ENO scheme based on the modified smoothness indicator

Cited by 9 publications

References 18 publications

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

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