Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
Journal of Computational Physics
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Use of a rotated Riemann solver for the two-dimensional Euler equations
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Methods for the accurate computations of hypersonic flows: I. AUSMPW + scheme
Journal of Computational Physics
Grid convergence of high order methods for multiscale complex unsteady viscous compressible flows
Journal of Computational Physics
On the implicit large eddy simulations of homogeneous decaying turbulence
Journal of Computational Physics
Journal of Computational Physics
An improved reconstruction method for compressible flows with low Mach number features
Journal of Computational Physics
Multi-dimensional limiting process for three-dimensional flow physics analyses
Journal of Computational Physics
Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids
Journal of Computational Physics
A new approach of a limiting process for multi-dimensional flows
Journal of Computational Physics
Scale separation for implicit large eddy simulation
Journal of Computational Physics
Journal of Computational Physics
Multi-dimensional limiting for high-order schemes including turbulence and combustion
Journal of Computational Physics
Journal of Scientific Computing
Hi-index | 31.49 |
Through the analysis of conventional TVD limiters, a new multi-dimensional limiting function is derived for an oscillation control in multi-dimensional flows. And, multi-dimensional limiting process (MLP) is developed with the multi-dimensional limiting function. The major advantage of MLP is to prevent oscillations across a multi-dimensional discontinuity, and it is readily compatible with more than third order spatial interpolation. Moreover, compared with other higher order interpolation schemes such as ENO type schemes, MLP shows a good convergence characteristic in a steady problem and it is very simple to be implemented. In the present paper, third and fifth order interpolation schemes with MLP, named MLP3 and MLP5, are developed and tested for several real applications. Through extensive numerous test cases including an oblique stationary contact discontinuity, an expansion fan, a vortex flow, a shock wave/vortex interaction and a viscous shock tube problem, it is verified that MLP combined with M-AUSMPW+ numerical flux substantially improves accuracy, efficiency and robustness both in continuous and discontinuous flows. By extending the current approach to three-dimensional flows, MLP is expected to reduce computational cost and enhance accuracy even further.