Summary
The flux-corrected transport (FCT) methodology is generalized to implicit finite element schemes and applied to the Euler equations of gas dynamics. The underlying low-order scheme is constructed by applying scalar artificial viscosity proportional to the spectral radius of the cumulative Roe matrix. All conservative matrix manipulations are performed edge-by-edge which leads to an efficient algorithm for the matrix assembly. The outer defect correction loop is equipped with a block-diagonal preconditioner so as to decouple the discretized Euler equations and solve all equations individually. As an alternative, a strongly coupled solution strategy is investigated in the context of stationary problems which call for large time steps.
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Möller, M., Kuzmin, D., Turek, S. (2004). Implicit FEM-FCT algorithm for compressible flows. In: Feistauer, M., DolejÅ¡Ã, V., Knobloch, P., Najzar, K. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18775-9_62
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DOI: https://doi.org/10.1007/978-3-642-18775-9_62
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