VERIFICATION OF AN HYPERSONIC FLOW SOLVER USING DISCONTINUOUS MANUFACTURED SOLUTIONS

SALDÍA, JUAN; ELASKAR, SERGIO

Santa Fe

Conferencia; XXIV Congreso sobre Métodos Numéricos y sus Aplicaciones ENIEF 2019; 2019

Asociación Argentina de Mecánica Computacional

The method of manufactured solutions (MMS) is a widely used technique applied to the ver-ification of computational software for the numerical modeling of physical systems, that is, the processby which certainty that the numerical algorithms of the model are correctly implemented is obtained.In the MMS, the original governing equations of the model are modified through the introduction ofan analytically derived source term, such that the numerical solution of the modified model convergesto a prescribed manufactured solution. When applied to mesh-based computational mechanics codes,the MMS generally introduces the requirement of a volumetric integration of an analytical expression atthe mesh element level. The usage of discontinuous manufactured solutions in the MMS, required forthe verification of numerical models where discontinuities naturally arise, has been addressed only infew works. Previous efforts in this direction, have focused only on particular cases in two dimensionaldomains, or when the manufactured solution is simple enough to allow the computation of exact inte-grals through symbolic manipulation engines. In the present work, we have applied recent techniques forthe high-order numerical integration of discontinuous solutions introduced in T-P. Fries et.al., Int J NumMeth Eng, 106:323-371 (2015), to the MMS based verification process of an in-house second order finitevolume solver with shock-capturing schemes for the numerical simulation of hypersonic thermochem-ical non-equilibrium flows. A high-order reconstruction of a level set based implicit description of thediscontinuity surface is first obtained, serving as the basis for the volumetric integration of the additionalsource terms introduced by the MMS, on those elements crossed by discontinuities. A generic frame-work has been implemented for the employment of this technique in unstructured mesh discretizationsof both 2D and 3D computational domains. Finally, results regarding the MMS verification process thathas been carried out are obtained and discussed.