A third-order compact finite volume scheme on unstructured grid for fluid flows

Abstract

The large reconstruction stencil is one of the biggest obstacles in design and implementation of high-order finite volume schemes on unstructured grid. To tackle this problem, a third-order compact reconstruction scheme on unstructured grid is developed on the basis of compact least-squares (CLS) finite volume method. In building the reconstruction polynomial, the general boundary condition is adopted to ensure the unified third-order accuracy in both the internal and boundary cells. The reconstruction polynomial is solved in a semi-implicit sense to ensure high computational efficiency without solving the global linear algebraic equations. The theoretical accuracy order and stability limit are firstly verified by the Fourier analysis. The numerical accuracy and efficiency are then verified and validated with several incompressible and compressible flow cases. This work provides a reference to design and analysis of high-order compact finite volume schemes on unstructured grid with unified accuracy.