Paul Maximum Principle Study Hydrodynamics Algorithm Multi-media Content

Numerical Simulation for the problems of Multi-component fluid dynamics is an important topic in the research of Computational Fluid Dynamics. How-ever, when applying the existing algorithms for the Euler Equations of single-component flow to the numerical simulation of multi-component, three difficul-ties occur:first, the mass fraction of Multi-component flows becomes negative, same thing happens to the volume fraction occasionally; second, the non-physical oscillation of pressure occurs in the discontinuity of contact; third, these existing algorithms are seldom applicable to the higher-order scenarios and other equa-tions of state for a certain non-ideal gaseous mixture.Many numerical algorithms have been worked out in trying to solve these difficulties, but none of them can solve the three difficulties simultaneously. For example, Abgrall[1] had guaranteed the positivity of mass fractions for the equa-tions of state for an ideal gaseous mixture and well handled the oscillation of pressure at the discontinuity of contact. But his method can hardly be applied to the higher order scenario and for the non-ideal gaseous mixture. While Saurel and Abgrall [8]’s numerical method for the resolution of conservation equations relies on the introduction of volume fraction; this method is also applicable to compute equations of state of rigid gas. Based on Abgrall’s achievements, Shyue K.M [9-11] had developed an efficient shock-capturing algorithm for compressible multi-component problems; he had made numerical simulation based on WPA, but his method cannot guarantee the positivity of volume fraction. Larrouturou [12] considered a hyperbolic system including the Euler equations for the mixture and a mass conservation equation for each species and proposed a new approxima-tion scheme for the convective term of the species equations. This approximation, whose construction relies on some properties of the exact solution of the Riemann problem for the multi-component system, uses an upwind Godunov-type scheme for the Euler equations. Its main interest lies in the fact that it preserves the positivity and monotonicity of the mass fractions of all species, but this approx- imation is not good enough at handling the oscillation of pressure occurring in the discontinuity of contact.Based on the above achievements and deficiencies, this paper did some re-search on the numerical simulation of Multi-component fluid dynamics for equa-tions of state for a certain non-ideal gaseous mixture with the guarantee of pos-itivity of mass fraction. This simulation contains classic Euler equations, equa-tions of conservation of mass fractions, and equations of conservation of material parameters. The simulation is written in the manner of conservative form, and using of high-order Wave propagation algorithms and the application of the max-imum principle for mass fractions to modify the corresponding parameters’values in order to acquire a numerical algorithm that can be applied to high-order equa-tions. Based on the results of Mie-Gruneisen equations of state, this algorithm can be applied to equations of state of rigid gaseous mixture.