Abstract
The large reconstruction stencil has been the major bottleneck problem in developing high order finite volume schemes on unstructured grids. This paper presents a compact reconstruction procedure for arbitrarily high order finite volume method on unstructured grids to overcome this shortcoming. In this procedure, a set of constitutive relations are constructed by requiring the reconstruction polynomial and its derivatives on the control volume of interest to conserve their averages on face-neighboring cells. These relations result in an over-determined linear equation system, which, in the sense of least-squares, can be reduced to a block-tridiagonal system in the one-dimensional case. The one-dimensional formulations of the reconstruction are discussed in detail and a Fourier analysis is presented to study the dispersion/dissipation and stability properties. The WBAP limiter based on the secondary reconstruction is used to suppress the non-physical oscillations near discontinuities while achieve high order accuracy in smooth regions of the solution. Numerical results demonstrate the method's high order accuracy, robustness and shock capturing capability. A new reconstruction procedure for high order finite volume scheme is proposed.This procedure can achieve arbitrary order of accuracy using a compact stencil consisting of only face neighboring cells.The spectral properties of the proposed finite volume schemes are analyzed.Some test cases are solved numerically to show the superior performances of the proposed schemes.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.