Efficient implementation of WENO schemes to nonuniform meshes |
| |
Authors: | Nelida ?rnjari?-?ic Senka Ma?e?i? Bojan Crnkovi? |
| |
Institution: | (1) Faculty of Engineering, University of Rijeka, Rijeka, Croatia |
| |
Abstract: | Most of the standard papers about the WENO schemes consider their implementation to uniform meshes only. In that case the
WENO reconstruction is performed efficiently by using the algebraic expressions for evaluating the reconstruction values and
the smoothness indicators from cell averages. The coefficients appearing in these expressions are constant, dependent just
on the scheme order, not on the mesh size or the reconstruction function values, and can be found, for example, in Jiang and
Shu (J Comp Phys 126:202–228, 1996). In problems where the geometrical properties must be taken into account or the solution
has localized fine scale structure that must be resolved, it is computationally efficient to do local grid refinement. Therefore,
it is also desirable to have numerical schemes, which can be applied to nonuniform meshes. Finite volume WENO schemes extend
naturally to nonuniform meshes although the reconstruction becomes quite complicated, depending on the complexity of the grid
structure. In this paper we propose an efficient implementation of finite volume WENO schemes to nonuniform meshes. In order
to save the computational cost in the nonuniform case, we suggest the way for precomputing the coefficients and linear weights
for different orders of WENO schemes. Furthermore, for the smoothness indicators that are defined in an integral form we present
the corresponding algebraic expressions in which the coefficients obtained as a linear combination of divided differences
arise. In order to validate the new implementation, resulting schemes are applied in different test examples.
|
| |
Keywords: | Nonuniform mesh Finite volume WENO schemes Hyperbolic balance law Open-channel flow equations Allievi’ s equations |
本文献已被 SpringerLink 等数据库收录! |
|