High Order Residual Distribution Schemes Based on Multidimensional Upwinding

Villedieu, N.; Quintino, Tiago; Vymazal, Martin; Deconinck, H.

doi:10.1007/978-3-642-03707-8_10

Cited by 1 publication

(1 citation statement)

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“…Relatively little work has been reported on the contribution of high‐order grids to the accuracy of numerical methods. Comparisons of the numerical error generated with the use of high‐order and low‐order 2D grids have been presented . However, there is still a need to compare the numerical error of high‐order 3D grids with that of conventional low‐order ones.…”

Section: Introductionmentioning

confidence: 99%

A study of properties of adaptive quadratic grids for three‐dimensional near‐surface field computations

Kallinderis

Lymperopoulou

Spyridonos

et al. 2019

Numerical Methods in Fluids

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Summary Curved geometries and the corresponding near‐surface fields typically require a large number of linear computational elements. High‐order numerical solvers have been primarily used with low‐order meshes. There is a need for curved, high‐order computational elements. Typical near‐surface meshes consist of hexahedral and/or prismatic elements. The present work studies the employment of quadratic meshes that are relatively coarse for field simulations. Directionally quadratic high‐order elements are proposed for the near‐surface field regions. The quadratic meshes are compared with the conventional low‐order ones in terms of accuracy and efficiency. The cases considered include closed surface volume calculations, as well as computation of gradients of several analytic fields. A special method of adaptive local quadratic meshes is proposed and evaluated. Truncation error analysis for quadratic grids yields comparison with the conventional linear hexahedral/prismatic meshes, which are subject to typical distortions such as stretching, skewness, and torsion.

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Section: Introductionmentioning

confidence: 99%