Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids III: One Dimensional Systems and Partition Optimization

In this paper, the third in a series, the Spectral Volume (SV) method is extended to one-dimensional systems—the quasi-1D Euler equations. In addition, several new partitions are identified which optimize a certain form of the Lebesgue constant, and the performance of these partitions is assessed with the linear wave equation. A major focus of this paper is to verify that the SV method is capable of achieving high-order accuracy for hyperbolic systems of conservation laws. Both steady state and time accurate problems are used to demonstrate the overall capability of the SV method.

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