Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
A class of implicit upwind schemes for Euler simulations with unstructured meshes
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Convergence to steady state solutions of the Euler equations on unstructured grids with limiters
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
Methods for the accurate computations of hypersonic flows: I. AUSMPW + scheme
Journal of Computational Physics
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation
Journal of Computational Physics
Cures for the shock instability: development of a shock-stable Roe scheme
Journal of Computational Physics
Resolution of high order WENO schemes for complicated flow structures
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Weighted essentially non-oscillatory schemes on triangular meshes
Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows
Journal of Computational Physics
Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
Journal of Scientific Computing
Multi-dimensional limiting process for three-dimensional flow physics analyses
Journal of Computational Physics
Journal of Computational Physics
Multi-dimensional limiting for high-order schemes including turbulence and combustion
Journal of Computational Physics
The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids
Journal of Computational Physics
Hi-index | 31.46 |
The present paper deals with an efficient and accurate limiting strategy for the multi-dimensional hyperbolic conservation laws on unstructured grids. The multi-dimensional limiting process (MLP) which has been successfully proposed on structured grids is extended to unstructured grids. The basic idea of the proposed limiting strategy is to control the distribution of both cell-centered and cell-vertex physical properties to mimic multi-dimensional nature of flow physics, which can be formulated to satisfy so called the MLP condition. The MLP condition can guarantee high-order spatial accuracy and improved convergence without yielding spurious oscillations. Starting from the MUSCL-type reconstruction on unstructured grids followed by the efficient implementation of the MLP condition, MLP slope limiters on unstructured meshes are obtained. Thanks to its superior limiting strategy and maximum principle satisfying characteristics, the newly developed MLP on unstructured grids is quite effective in controlling numerical oscillations as well as accurate in capturing multi-dimensional flow features. Numerous test cases are presented to validate the basic features of the proposed approach.