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A ug 2 00 9 All speed scheme for the low mach number limit of the Isentropic Euler equation
| Content Provider | Semantic Scholar |
|---|---|
| Author | Degond, Pierre Tang, Min |
| Copyright Year | 2009 |
| Abstract | An all speed scheme for the Isentropic Euler equation is pres ent d in this paper. When the Mach number tends to zero, the compressi bl Euler equation converges to its incompressible counterpart, in w hich the density becomes a constant. Increasing approximation errors and se vere stability constraints are the main difficulty in the low Mach regime. Th e key idea of our all speed scheme is the special semi-implicit time dis cretization, in which the low Mach number stiff term is divided into two parts , one being treated explicitly and the other one implicitly. Moreov er, the flux of the density equation is also treated implicitly and an elliptic type equation is derived to obtain the density. In this way, the correct limit can be captured without requesting the mesh size and time step to be smaller t han the Mach number. Compared with previous semi-implicit methods [11, 13, 27], nonphysical oscillations can be suppressed. We develop this se mi-implicit time discretization in the framework of a first order local Lax-Fr iedrich (LLF) scheme and numerical tests are displayed to demonstrate its p rformances. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/0908.1929v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Approximation Arabic numeral 0 Choose (action) Courant–Friedrichs–Lewy condition Cure for Lymphoma Foundation Discretization Euler Flow Han unification Limbo Local Area Networks Numerical analysis Population Parameter Semiconductor industry Shock Small density |
| Content Type | Text |
| Resource Type | Article |
