A Taylor-series approach to numerical accuracy and a third-order scheme for strong convective flows

Abstract The use of the Taylor-series theorem to study the accuracy of numerical discretization shemes is re-examined. A generalized equation is presented for a given derivative, to any required order of accuracy. The relationship between the Taylor-series truncation errors (TSTE) of each term in the parent differential equation and the solution error at each node is established through the concept of an inevitable error. Based on Taylor-series error analysis, a stable, third-order accurate numerical method for the convection term is presented which involves the same number of computational nodes as the second-order QUICK scheme. A two-dimensional test problem shows the new scheme generally to produce smaller solution and inevitable errors than other schemes.