High Order Finite Volume Nonlinear Schemes for the Boltzmann Transport Equation
The authors apply the nonlinear WENO (Weighted Essentially Nonoscillatory) scheme to the spatial discretization of the Boltzmann Transport Equation modeling linear particle transport. The method is a finite volume scheme which ensures not only conservation, but also provides for a more natural handling of boundary conditions, material properties and source terms, as well as an easier parallel implementation and post processing. It is nonlinear in the sense that the stencil depends on the solution at each time step or iteration level. By biasing the gradient calculation towards the stencil with smaller derivatives, the scheme eliminates the Gibb's phenomenon with oscillations of size O(1) and reduces them to O(h{sup r}), where h is the mesh size and r is the order of accuracy. The current implementation is three-dimensional, generalized for unequally spaced meshes, fully parallelized, and up to fifth order accurate (WENO5) in space. For unsteady problems, the resulting nonlinear spatial discretization yields a set of ODE's in time, which in turn is solved via high order implicit time-stepping with error control. For the steady-state case, they need to solve the non-linear system, typically by Newton-Krylov iterations. There are several numerical examples presented to demonstrate the accuracy, non-oscillatory nature and efficiency of these high order methods, in comparison with other fixed-stencil schemes.
- Research Organization:
- Lawrence Livermore National Lab., Livermore, CA (US)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 15015871
- Report Number(s):
- UCRL-PROC-210944
- Country of Publication:
- United States
- Language:
- English
Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws
|
book | January 1998 |
Subcell balance methods for radiative transfer on arbitrary grids
|
journal | January 1997 |
High resolution schemes for hyperbolic conservation laws
|
journal | March 1983 |
Uniformly high order accurate essentially non-oscillatory schemes, III
|
journal | August 1987 |
Similar Records
An Eulerian–Lagrangian Weighted Essentially Nonoscillatory scheme for nonlinear conservation laws
Denovo--A New Three-Dimensional Parallel Discrete Ordinates Code in SCALE