High‐order isogeometric modified method of characteristics for two‐dimensional coupled Burgers' equations

Abstract

Abstract This paper presents a novel isogeometric modified method of characteristics for the numerical solution of the two‐dimensional nonlinear coupled Burgers' equations. The method combines the modified method of characteristics and the high‐order NURBS () elements to discretize the governing equations. The Lagrangian interpretation in this isogeometric analysis greatly reduces the time truncation errors in the Eulerian methods. A third‐order explicit Runge–Kutta scheme is used for the discretization in time. We present a detailed description of the algorithm used for the calculation of departure points and the interpolation stage. Our focus is on constructing highly accurate and stable solvers for the two‐dimensional nonlinear coupled Burgers' equations at high Reynolds numbers. A variety of benchmark tests and numerical examples are provided to show the effectiveness, accuracy, and performance of the proposed modified method of characteristics by virtue of potential advantages of isogeometric analysis. The method developed is anticipated to provide new research directions to the practical calculation of incompressible flows and to studies of their physical behavior.