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 P1 – P1b – P1 and P2 – P2b – P2 for density – velocity – pressure were compared at AOA=1.25 and Mach number 0.8. As a result, the shock wave is not found on the upper – end 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.