Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
Journal of Computational Physics
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
Use of a rotated Riemann solver for the two-dimensional Euler equations
Journal of Computational Physics
Multidimensional upwinding. Part I. The method of transport for solving the Euler equations
Journal of Computational Physics
Journal of Computational Physics
Two-dimensional Riemann solver for Euler equations of gas dynamics
Journal of Computational Physics
Residual Distribution Schemes for Conservation Laws via Adaptive Quadrature
SIAM Journal on Scientific Computing
Finite volume evolution Galerkin methods for nonlinear hyperbolic systems
Journal of Computational Physics
A GENUINELY MULTIDIMENSIONAL UPWIND SCHEME AND EFFICIENT MULTIGRID SOLVER FOR THE COMPRESSIBLE EULER EQUATIONS
High Order Fluctuation Schemes on Triangular Meshes
Journal of Scientific Computing
An upwind finite difference scheme for meshless solvers
Journal of Computational Physics
Diffusion regulation for Euler solvers
Journal of Computational Physics
Meshless methods for computational fluid dynamics
Meshless methods for computational fluid dynamics
SIAM Journal on Numerical Analysis
Hi-index | 31.45 |
A computational tool called ''Directional Diffusion Regulator (DDR)'' is proposed to bring forth real multidimensional physics into the upwind discretization in some numerical schemes of hyperbolic conservation laws. The direction based regulator when used with dimension splitting solvers, is set to moderate the excess multidimensional diffusion and hence cause genuine multidimensional upwinding like effect. The basic idea of this regulator driven method is to retain a full upwind scheme across local discontinuities, with the upwind bias decreasing smoothly to a minimum in the farthest direction. The discontinuous solutions are quantified as gradients and the regulator parameter across a typical finite volume interface or a finite difference interpolation point is formulated based on fractional local maximum gradient in any of the weak solution flow variables (say density, pressure, temperature, Mach number or even wave velocity etc.). DDR is applied to both the non-convective as well as whole unsplit dissipative flux terms of some numerical schemes, mainly of Local Lax-Friedrichs, to solve some benchmark problems describing inviscid compressible flow, shallow water dynamics and magneto-hydrodynamics. The first order solutions consistently improved depending on the extent of grid non-alignment to discontinuities, with the major influence due to regulation of non-convective diffusion. The application is also experimented on schemes such as Roe, Jameson-Schmidt-Turkel and some second order accurate methods. The consistent improvement in accuracy either at moderate or marked levels, for a variety of problems and with increasing grid size, reasonably indicate a scope for DDR as a regular tool to impart genuine multidimensional upwinding effect in a simpler framework.