Economically high‐order unstructured‐grid methods: Clarification and efficient FSR schemes
Hiroaki Nishikawa
Abstract
Abstract In this article, we clarify reconstruction‐based discretization schemes for unstructured grids and discuss their economically high‐order versions, which can achieve high‐order accuracy under certain conditions at little extra cost. The clarification leads to one of the most economical approaches: the flux‐and‐solution‐reconstruction (FSR) approach, where highly economical schemes can be constructed based on an extended ‐scheme combined with economical flux reconstruction formulas, achieving up to fifth‐order accuracy (sixth‐order with zero dissipation) when a grid is regular. Various economical FSR schemes are presented and their formal orders of accuracy are verified by numerical experiments.
Topics & Concepts
DiscretizationGridMathematical optimizationScheme (mathematics)Computer scienceMathematicsUnstructured gridZero (linguistics)AlgorithmFlux limiterApplied mathematicsNumerical analysisRegular gridComputational fluid dynamicsMesh generationComputational Fluid Dynamics and AerodynamicsAdvanced Numerical Methods in Computational MathematicsModel Reduction and Neural Networks