caa a22 4500 378875019 CHVBK 20180305123418.0 cr unu---uuuuu 161128s2003 xx s 000 0 eng 10.2478/cmam-2003-0039 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2003-0039 A Highly Accurate Modified Method of Characteristics for Convection-dominated Flow Problems [Elektronische Daten] High-order accurate methods for convection-dominated flow problems have the potential to reduce the computational effort required for a given order of solution accuracy. The state of the art in this field is more advanced for Eulerian methods than for semi-Lagrangian methods. In this paper, we introduce a new higher order approach that is based on combining the modified method of characteristics with the gradients computed during solution reconstruction. Special attention is given to the class of third-order schemes which uses a higher-order method to calculate the departure points and a high-order polynomial reconstruction to interpolate the solution at the characteristic feet. Numerical experiments are carried out on several benchmark transport-diffusion equations including incompressible Navier-Stokes problems. The computed results support our expectations for a robust and high-order accurate method. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. modified method of characteristics nationallicence higher order advective schemes nationallicence advection-diffusion equations nationallicence incompressible Navier-Stokes problems nationallicence Machmoum Ahmed Facult´e des Sciences, LIMI, Universit´e Ibn Zohr, B.P. 28/S Agadir, Morocco. Seaïd Mohammed Fachbereich Mathematik, TU Darmstadt, 64289 Darmstadt, Germany. Computational Methods in Applied Mathematics De Gruyter 3/4(2003), 623-646 1609-4840 3:4<623 2003 3 cmam https://doi.org/10.2478/cmam-2003-0039 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2003-0039 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Machmoum Ahmed Facult´e des Sciences, LIMI, Universit´e Ibn Zohr, B.P. 28/S Agadir, Morocco NATIONALLICENCE 700 1- Seaïd Mohammed Fachbereich Mathematik, TU Darmstadt, 64289 Darmstadt, Germany NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 3/4(2003), 623-646 1609-4840 3:4<623 2003 3 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter