Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
SIAM Journal on Numerical Analysis
The convergence rate of approximate solutions for nonlinear scalar conservation laws
SIAM Journal on Numerical Analysis
Classification of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Mathematical Analysis
Nonconservative hybrid shock capturing schemes
Journal of Computational Physics
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
The convergence rate of Godunov type schemes
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A projection method for locally refined grids
Journal of Computational Physics
SIAM Journal on Scientific Computing
Pointwise Error Estimates for Scalar Conservation Laws with Piecewise Smooth Solutions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Space---Time Adaptive Solution of First Order PDES
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
New adaptive artificial viscosity method for hyperbolic systems of conservation laws
Journal of Computational Physics
Hi-index | 31.47 |
The formation of shock waves in solutions of hyperbolic conservation laws calls for locally adaptive numerical solution algorithms and requires a practical tool for identifying where adaption is needed. In this paper, a new smoothness indicator (SI) is used to identify "rough" solution regions and is implemented in locally adaptive algorithms. The SI is based on the weak local truncation error of the approximate solution. It was recently reported in S. Karni and A. Kurganov, Local error analysis for approximate solutions of hyperbolic conservation laws, where error analysis and convergence properties were established. The present paper is concerned with its implementation in scheme adaption and mesh adaption algorithms. The SI provides a general framework for adaption and is not restricted to a particular discretization scheme. The implementation in this paper uses the central-upwind scheme of A. Kurganov, S. Noelle, and G. Petrova, SIAM J. Sci. Comput. 23, 707 (2001). The extension of the SI to two space dimensions is given. Numerical results in one and two space dimensions demonstrate the robustness of the proposed SI and its potential in reducing computational costs and improving the resolution of the solution.