Name
Abstract | ||
|---|---|---|
This paper presents a model which provides a smooth transition between a kinetic and a diffusion domain. The idea is to use a buffer zone, in which both diffusion and kinetic equations will be solved. The solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations. We use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone. Thus no boundary condition is needed at the transition point. This model avoids the delicate issue of finding the interface condition or iteration in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations. A new asymptotic-preserving method for this model is introduced, and numerical examples are used to validate this new model and the new numerical method. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1137/S0036142903430414 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
boundary condition,diffusion domain,smooth transition,asymptotic preserving schemes,original kinetic equation,new model,diffusion approximation,new numerical method,kinetic-fluid coupling,new asymptotic-preserving method,typical domain decomposition method,buffer zone,transport equation,kinetic equation,diffusion equations,hydrodynamic equation,kinetics,numerical method,diffusion equation | Boundary value problem,Convection–diffusion equation,Mathematical analysis,Initial value problem,Partial differential equation,Mathematics,Multigrid method,Independent equation,Diffusion equation,Domain decomposition methods | Journal |
Volume | Issue | ISSN |
42 | 6 | 0036-1429 |
Citations | PageRank | References |
20 | 4.03 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pierre Degond | 1 | 251 | 43.75 |
| Shi Jin | 2 | 572 | 85.54 |
| Luc Mieussens | 3 | 195 | 22.01 |