A simple high-resolution advection scheme Export

@article{citeulike:2328868, abstract = {A simple, robust, mass-conserving numerical scheme for solving the linear advection equation is described. The scheme can estimate peak solution values accurately even in regions where spatial gradients are high. Such situations present a severe challenge to classical numerical algorithms. Attention is restricted to the case of pure advection in one and two dimensions since this is where past numerical problems have arisen. The authors' scheme is of the Godunov type and is second-order in space and time. The required cell interface fluxes are obtained by MUSCL interpolation and the exact solution of a degenerate Riemann problem. Second-order accuracy in time is achieved via a Runge-Kutta predictor-corrector sequence. The scheme is explicit and expressed in finite volume form for ease of implementation on a boundary-conforming grid. Benchmark test problems in one and two dimensions are used to illustrate the high-spatial accuracy of the method and its applicability to non-uniform grids. Copyright {\copyright} 2007 John Wiley \& Sons, Ltd.}, address = {Centre for Mathematical Modelling and Flow Analysis, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, U.K.; Department of Computing and Mathematics, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, U.K.}, author = {Mingham, C. G. and Causon, D. M.}, citeulike-article-id = {2328868}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/fld.1536}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/114276302/ABSTRACT}, doi = {10.1002/fld.1536}, journal = {International Journal for Numerical Methods in Fluids}, keywords = {numerical-methods}, number = {5}, pages = {469--484}, posted-at = {2008-02-04 09:32:16}, priority = {3}, title = {A simple high-resolution advection scheme}, url = {http://dx.doi.org/10.1002/fld.1536}, volume = {56}, year = {2008} }

TY - JOUR ID - citeulike:2328868 L3 - citeulike-article-id:2328868 N2 - A simple, robust, mass-conserving numerical scheme for solving the linear advection equation is described. The scheme can estimate peak solution values accurately even in regions where spatial gradients are high. Such situations present a severe challenge to classical numerical algorithms. Attention is restricted to the case of pure advection in one and two dimensions since this is where past numerical problems have arisen. The authors' scheme is of the Godunov type and is second-order in space and time. The required cell interface fluxes are obtained by MUSCL interpolation and the exact solution of a degenerate Riemann problem. Second-order accuracy in time is achieved via a Runge-Kutta predictor-corrector sequence. The scheme is explicit and expressed in finite volume form for ease of implementation on a boundary-conforming grid. Benchmark test problems in one and two dimensions are used to illustrate the high-spatial accuracy of the method and its applicability to non-uniform grids. Copyright © 2007 John Wiley & Sons, Ltd. IS - 5 JF - International Journal for Numerical Methods in Fluids AD - Centre for Mathematical Modelling and Flow Analysis, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, U.K.; Department of Computing and Mathematics, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, U.K. EP - 484 TI - A simple high-resolution advection scheme VL - 56 SP - 469 KW - numerical-methods AU - Mingham, CG AU - Causon, DM PY - 2008/// UR - http://dx.doi.org/10.1002/fld.1536 ER -