Finite Difference Hermite WENO Schemes for Conservation Laws, II: An Alternative Approach

Liu, Hongxia; Qiu, Jianxian

doi:10.1007/s10915-015-0041-4

Cited by 47 publications

(16 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A comparison of the relative efficiency between the finite volume and DG schemes is given in [287]. There are also intermediate methods between DG and finite volume schemes, which have more than one degrees of freedom per cell yet not enough for the full k-th degree polynomial, hence still require a reconstruction which however has a smaller stencil than that for regular DG schemes, such as the Hermite-type finite volume and finite difference schemes [184,185,151], the recovery-type DG schemes [226,227], and the P n P m type methods [63,62]. If the high memory requirement of DG is a concern, these intermediate methods might be good options.…”

Section: Discontinuous Galerkin and Related Schemesmentioning

confidence: 99%

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

Shu

2016

Journal of Computational Physics

166

View full text Add to dashboard Cite

For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, namely the weighted essentially non-oscillatory (WENO) finite difference and finite volume schemes and discontinuous Galerkin (DG) finite element methods, emphasizing several of their recent developments: bound-preserving limiters for DG, finite volume and finite difference schemes, which address issues in robustness and accuracy; WENO limiters for DG methods, which address issues in non-oscillatory performance when there are strong shocks, and inverse Lax-Wendroff type boundary treatments for finite difference schemes, which address issues in solving complex geometry problems using Cartesian meshes.

show abstract

Section: Discontinuous Galerkin and Related Schemesmentioning

confidence: 99%

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

Shu

2016

Journal of Computational Physics

166

View full text Add to dashboard Cite

show abstract

“…Liu [21] conducted a comparative study for the fifth-order alternative WENO scheme using different approximate Riemann solver for inviscid cases. The alternative methodology has also been used with the compact-WENO scheme [22], and the Hermite WENO scheme [23]. The alternative WENO approach could not perform with optimal accuracy at the points where derivatives become zero (critical points).…”

Section: Introductionmentioning

confidence: 99%

A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws

Rajput¹,

Singh²

2022

AAMM

View full text Add to dashboard Cite

“…In Reference [14], Cravero and Semplice presented the third‐order CWENO schemes for hyperbolic conservation and balance laws on nonuniform meshes. For more details, see Reference [15‐18] and the references included.…”

Section: Introductionmentioning

confidence: 99%

A new ninth‐order central Hermite weighted essentially nonoscillatory scheme for hyperbolic conservation laws

Zahran

Abdalla

2020

Numerical Methods in Fluids

View full text Add to dashboard Cite

In this article, we propose a new ninth‐order central Hermite weighted essentially nonoscillatory (HWENO) scheme, for solving hyperbolic conservation laws. The new scheme consists of the following: ninth‐order reconstruction using only five points stencil; to calculate the linear weights we used the central WENO (CWENO) technique and for nonlinear weights we used a new weighting technique. The numerical solution is advanced in time by using the ninth‐order linear strong‐stability‐preserving Runge–Kutta (ℓSSPRK) scheme and for computing the numerical flux, we used the central‐upwind flux which is efficient, simple and can be used for nonconex fluxes problems. The resulting scheme is ninth order in both smooth regions and at critical points with very small numerical dissipation near discontinuities, this is due to using new smoothness indicators. Several numerical examples are presented for one‐ and two‐dimensional problems to confirm that the new scheme is superior to the other high‐order WENO schemes.

show abstract

Finite Difference Hermite WENO Schemes for Conservation Laws, II: An Alternative Approach

Cited by 47 publications

References 26 publications

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws

A new ninth‐order central Hermite weighted essentially nonoscillatory scheme for hyperbolic conservation laws

Contact Info

Product

Resources

About