New calculation scheme for compressible Euler equation

Abstract

In this paper, numerical demonstrations of a modified compressible Euler system are shown, where the bubble function element stabilization method together with adaptive mesh refinement is introduced for increasing numerical stability and numerical accuracy. For a test case, NACA0012 is selected as a domain of interest, and numerical results using finite elements of P1­P1b­P1 and P2­P2b­P2 for density­velocity­pressure were compared at AOA=1.25 and Mach number 0.8. As a result, the shock wave is not found on the upper­end and the lower­ end of NACA0012 in the former, and on the other hand the latter is adequate numerical result and relative errors of Cl, Cd with previous study are 1.197% and 0.15376%. The mathematical model is much simpler than the compressible Euler equation, because they are advection equations for a density, a velocity, and a pressure with each external forces. Therefore, the material derivative is considered for time stepping, and the characteristic curve method can be used for decreasing calculation cost.

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