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 timeharmonic domain for an arbitrary flow with high order finite element methods. Several equivalent formulations of Galbrun’s equations are proposed and discretized with Discontinuous Galerkin method. They are compared with a formulation adapted for continuous Galerkin discretization. Numerically, it has been observed that the tested discretization methods converge correctly for an uniform flow, but no longer for a non-uniform flow. Two kinds of stabilization are proposed in order to restore a nice convergence though original equations are modified. Finally, simplified Galbrun’s equations are proposed to coincide with original Galbrun’s equations when the flow is null. Numerical illustrations are presented in the context of helioseismology.
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Juliette Chabassier, Marc Durufle. 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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