Compact High Order Finite Volume Method and Its Application

Abstract

This paper presents a compact high-order finite volume method based on recording the weighted integral value of a function on a grid cell. Extending the general finite volume method, it employs a single unit template and a limiter method to suppress oscillations, addressing the convection-diffusion equation. By utilizing implicit methods for nonlinear and linear solvers of the discrete equation, the scheme achieves enhanced compactness, accuracy, and computational efficiency.