کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5011741 | 1462655 | 2017 | 8 صفحه PDF | دانلود رایگان |
- Contains an original method for discretizing two-dimensional parabolic PDE's based on Dirichlet-to-Neumann maps.
- Explores the resulting schemes when the PDE's are standard heat or anisotropic diffusion equations on a Cartesian grid.
- Derives numerical fluxes where external source terms are included into numerical fluxes.
A general methodology, which consists in deriving two-dimensional finite-difference schemes which involve numerical fluxes based on Dirichlet-to-Neumann maps (or Steklov-Poincaré operators), is first recalled. Then, it is applied to several types of diffusion equations, some being weakly anisotropic, endowed with an external source. Standard finite-difference discretizations are systematically recovered, showing that in absence of any other mechanism, like e.g. convection and/or damping (which bring Bessel and/or Mathieu functions inside that type of numerical fluxes), these well-known schemes achieve a satisfying multi-dimensional character.
Journal: Computers & Fluids - Volume 156, 12 October 2017, Pages 58-65