High Resolution Finite Volume Scheme Based on the Quintic Spline Reconstruction on Non-uniform Grids

High Resolution Finite Volume Scheme Based on the Quintic Spline Reconstruction on Non-uniform Grids This paper presents a compact quintic spline reconstruction for finite volume method on non-uniform structured grids. The primitive function of a dependent variable is reconstructed by a piece-wise quintic polynomial by requiring the derivatives up to fourth order being continuous at the cell interfaces. This procedure results in a block tridiagonal system of linear equations which can be solved efficiently by incorporating certain boundary closure relations. There are some distinct features in the quintic spline reconstruction. Firstly, the reconstruction stencil is compact; Secondly, the reconstruction can be applied on arbitrary non-uniform grids; and finally, the reconstruction is continuous at cell interface without the need of a Riemann solver. To stabilize the scheme, the sixth order artificial viscosity is introduced. The quintic spline reconstruction achieves sixth-order accuracy on uniform grids without artificial viscosity and fifth-order accuracy on both uniform and non-uniform grids when artificial viscosity is added. The splined scheme is blended with shock-capturing WENO scheme to suppress non-physical oscillations near discontinuities. Numerical results demonstrate the accuracy, robustness and efficiency of the proposed scheme. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

High Resolution Finite Volume Scheme Based on the Quintic Spline Reconstruction on Non-uniform Grids

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-017-0524-6
Publisher site
See Article on Publisher Site

Abstract

This paper presents a compact quintic spline reconstruction for finite volume method on non-uniform structured grids. The primitive function of a dependent variable is reconstructed by a piece-wise quintic polynomial by requiring the derivatives up to fourth order being continuous at the cell interfaces. This procedure results in a block tridiagonal system of linear equations which can be solved efficiently by incorporating certain boundary closure relations. There are some distinct features in the quintic spline reconstruction. Firstly, the reconstruction stencil is compact; Secondly, the reconstruction can be applied on arbitrary non-uniform grids; and finally, the reconstruction is continuous at cell interface without the need of a Riemann solver. To stabilize the scheme, the sixth order artificial viscosity is introduced. The quintic spline reconstruction achieves sixth-order accuracy on uniform grids without artificial viscosity and fifth-order accuracy on both uniform and non-uniform grids when artificial viscosity is added. The splined scheme is blended with shock-capturing WENO scheme to suppress non-physical oscillations near discontinuities. Numerical results demonstrate the accuracy, robustness and efficiency of the proposed scheme.

Journal

Journal of Scientific ComputingSpringer Journals

Published: Sep 11, 2017

References

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