Streamline Tracing Methods Based on Piecewise Polynomial Pressure Approximations

Abstract

In this paper, a unified approach for developing streamline tracing method is proposed based on piecewise polynomial pressure approximation functions. It is designed for the numerical schemes that solve the pressure solution at grid blocks while the interior velocity field remains unknown. The suitable velocity approximation functions are derived through analytical differentiation of pressure functions. They better represent the relationship between velocity field and pressure distribution in reality, satisfy the Laplace equation everywhere in a grid block, and ensure local mass conservation and normal flux continuity. Based on different polynomial pressure functions, the Trilinear/Bilinear and Cubic streamline tracing methods are developed. Additionally, a piecewise parabolic velocity reconstruction method is proposed to extend the application of the Cubic method to first-order numerical schemes. The accuracy and efficiency of the newly proposed methods are evaluated through comparing it with the Pollock and the high-order method in terms of velocity approximations and computational cost in numerical cases. Comparison results indicate that the Cubic method delivers the most accurate results at the same computational cost.