Solving time-harmonic Galbrun's equation with an arbitrary flow. Application to Helioseismology

Abstract : In this report, we are concerned with the solution of Galbrun’s equations in timeharmonicdomain for an arbitrary flow with high order finite element methods. Several equivalentformulations of Galbrun’s equations are proposed and discretized with Discontinuous Galerkinmethod. They are compared with a formulation adapted for continuous Galerkin discretization.Numerically, it has been observed that the tested discretization methods converge correctly foran uniform flow, but no longer for a non-uniform flow. Two kinds of stabilization are proposedin order to restore a nice convergence though original equations are modified. Finally, simplifiedGalbrun’s equations are proposed to coincide with original Galbrun’s equations when the flow isnull. Numerical illustrations are presented in the context of helioseismology.
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Juliette Chabassier, Marc Duruflé. Solving time-harmonic Galbrun's equation with an arbitrary flow. Application to Helioseismology. [Research Report] RR-9192, INRIA Bordeaux. 2018. ⟨hal-01833043⟩

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