Improvement of a solution of inviscid compressible flows using a mixed wall boundary condition

Abstract

Boundary conditions have a vital role in the numerical solution of the partial differential equations governing fluid flows, and they have a great influence over the numerical stability and accuracy of the final solutions. One of the most important physical boundary conditions in flow field analysis, especially for inviscid flows, is the wall boundary condition imposed on body surfaces. To solve a three-dimensional compressible Euler equation (with five PDE's), a total of five boundary conditions on the body surface should be prescribed. The wall's velocity magnitude is one of the parameters to be determined, and the way this velocity magnitude is calculated affects the accuracy and stability of the numerical approach. In this paper, four different methods for calculation of the wall velocity magnitude are introduced, tested and compared against several test cases of subsonic and supersonic flows. Since there are many problems where both subsonic and supersonic flows coexist, a mixed boundary condition takes into account the flow Mach number is proposed. The mixed boundary condition is applied to several test cases and the stability of the method is examined.