Relaxed High Resolution Schemes for Hyperbolic Conservation Laws

Authors:
H. Joachim Schroll
Affiliations:
Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden. achim.schroll@na.lu.se
Venue:
Journal of Scientific Computing
Year:
2004

Citing 12
Cited 5

Some results on uniformly high-order accurate essentially nonoscillatory schemes

Applied Numerical Mathematics - Special issue in honor of Milt Rose's sixtieth birthday
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II

Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws

Journal of Computational Physics
Classification of the Riemann problem for two-dimensional gas dynamics

SIAM Journal on Mathematical Analysis
Numerical solution of the Riemann problem for two-dimensional gas dynamics

SIAM Journal on Scientific Computing
Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws

SIAM Journal on Scientific Computing
New high-resolution central schemes for nonlinear conservation laws and convection—diffusion equations

Journal of Computational Physics
The third-order relaxation schemes for hyperbolic conservation laws

Journal of Computational and Applied Mathematics
High Resolution Schemes for Conservation Laws with Locally Varying Time Steps

SIAM Journal on Scientific Computing
Strong Stability-Preserving High-Order Time Discretization Methods

SIAM Review
High Resolution Relaxed Upwind Schemes in Gas Dynamics

Journal of Scientific Computing
On the construction, comparison, and local characteristic decomposition for high-Order central WENO schemes

Journal of Computational Physics

High Resolution Relaxed Upwind Schemes in Gas Dynamics

Journal of Scientific Computing
A Bi-Hyperbolic Finite Volume Method on Quadrilateral Meshes

Journal of Scientific Computing
Numerical simulation of Camassa-Holm peakons by adaptive upwinding

Applied Numerical Mathematics
Conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics

Journal of Computational Physics
Numerical simulation of Camassa--Holm peakons by adaptive upwinding

Applied Numerical Mathematics

Quantified Score

Hi-index	0.01

Visualization

Abstract

Relaxed, essentially non-oscillating schemes for nonlinear conservation laws are presented. Exploiting the relaxation approximation, it is possible to avoid the nonlinear Riemann problem, characteristic decompositions, and staggered grids. Nevertheless, convergence rates up to fourth order are observed numerically. Furthermore, a relaxed, piecewise hyperbolic scheme with artificial compression is constructed. Third order accuracy of this method is proved. Numerical results for two-dimensional Riemann problems in gas dynamics are presented. Finally, the relation to central schemes is discussed.