Derivative artificial compression method for conservation laws

摘要

Applying high resolution difference schemes on the derivative equationsrnof conservation laws could overcome the shortcoming of accuracy decay atrnextreme points that has plagued almost all high resolution schemes. Similar tornHarten’s artificial compression method, the new method is called as derivativernartificial compression method, which has high resolution, low dissipation and lowrndiffusion properties, and could enhance the resolution (of numerical solution) bothrnat discontinuities and at extreme points. Numerical experiments are implementedrnusing initial value problems of single conservation law, one dimensional shockrntube problem, two dimensional Riemann problem, double Mach reflection problemrnand flow around NACA0012 airfoil. Resolutions of discontinuities, extremes andrnfine structures are compared between original TVD schemes, schemes usingrnartificial compression method and schemes using derivative artificial compressionrnmethod.