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.


<pdf>Media:Draft_Content_640525130-1928_paper-3741-document.pdf</pdf>

== Document ==
<pdf>Media:Draft_Content_640525130-1928_paper-3254-document.pdf</pdf>