Numerical computation of the Shock Tube Problem by means of wave digital principles
[摘要] Partial differential equations can be solved numerically by means of wave digital principles.The great advantage of this method is the simultaneous achievement of high robustness, massive parallelismfull localness and high accuracy.Among others this method will be applied in order to solve the Euler-equations according to onedimension in space.Especially the so called Shock Tube Problem will be examined.The analytical solution of this problem contains two discontinuities, namely a shockand a contact discontinuity. These result in oscillations which are due to numerical integration methodsof higher order.Also solutions of the Wave Digital Method contain these oscillations, contrary to what had been observed of Yuhui Zhu (2000).This behaviour is also known as Gibbs Phenomena.
The Navier-Stokes-equations, which are from a physical point of viewmore exactly, additionally take viscosity terms into account. This leads to smooth solutions near shocks.It will be shown that this approach leads to the suppression of the oscillationsnear the shock. Furthermore it will be shown that quite good results for the computation of velocityand pressure can be obtained.
