A Very High-Order Spatial Lagrange Interpolating Polynomial Scheme

Abstract

This paper presents the extension of the Lagrange Interpolating Polynomial (LIP) scheme for solving differential equations by using the finite volume method called the Very high-order Spatial Lagrange Interpolating Polynomial (VS-LIP) scheme. The advantage of the VS-LIP scheme is its convenience for extending the order of accuracy. The correctness of the VS-LIP scheme solutions is assessed by comparing the solutions with analytical, benchmark, published, and experimental solutions of five verification problems involving one- and two-dimensional heat transfer and fluid flow. The assessment is carried out to the sixth and twelfth orders of spatial accuracy. The assessment results indicated that the VS-LIP scheme delivers the correct solutions.