An accurate and efficient finite element Euler equation algorithm
An implicit finite element algorithm is established for numerical solution of the multi-dimensional Euler equations. The theoretical construction employs a multi-pole expansion of the Galerkin-Weighted Residuals concept requiring the error in the semi-discrete (finite element) approximation to be rendered orthogonal to the finite dimensional sub space of H1 selected to generate the solution. Identification of the tensor matrix product resolution of the Newton iteration algorithm Jacobian, valid for arbitrary degree k of the approximation subspace, and a generalized-coordinates framework amenable to use with any regularizing coordinate transformation, renders the algorithm economically competitive. Numerical results document accurate solutions for mixed subsonic-supersonic flows, including robust resolution of shocks on rather coarse discretizations of Rn, as well as convergence estimates in H1 and E. The algorithm concept is equally applicable to the complete Navier-Stokes equations.
KeywordsComputational Fluid Dynamic Jacobian Formulation Finite Element Algorithm Coarse Discretizations Computational Fluid Dynamic Research
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