Author(s): Javier Murillo; Javier Burguete; Pilar Brufau; Pilar Garcia-Navarro
Linked Author(s): Pilar García-Navarro
Keywords: Semi-lagrangian method; Characteristic equations; Conservation; Advection; Interpolation
Abstract: The development of two-dimensional unstructured adaptative meshes has made possible a better resolution of real problems when special features of the fluid flow or complex geometries are present, but this is a challenge for high order numerical methods. An important effort has been done in improving the quality of the methods for convection dominated flows but they are not efficient in presence of discontinuities in unstructured meshes. A conservative semi-lagrangian technique is proposed in this work. Contrary to classical semi-lagrangian schemes which impose the conservation of the characteristic variable along the characteristic curves, in the proposed semi-lagrangian conservative schemes, the equation is solved imposing the propagation of the conserved variable contained in the full cell. After resolving the propagation of the grid cells, to achieve the conserved variable in the physical grid nodes without rating the conservation property of this method a conservative interpolation is performed.
Year: 2005