1. |
|
|
2. |
- Guermond, Jean-Luc, et al.
(författare)
-
Second-Order Invariant Domain Preserving Approximation of the Euler Equations Using Convex Limiting
- 2018
-
Ingår i: SIAM Journal on Scientific Computing. - : SIAM PUBLICATIONS. - 1064-8275 .- 1095-7197. ; 40:5, s. A3211-A3239
-
Tidskriftsartikel (refereegranskat)abstract
- A new second-order method for approximating the compressible Euler equations is introduced. The method preserves all the known invariant domains of the Euler system: positivity of the density, positivity of the internal energy, and the local minimum principle on the specific entropy. The technique combines a first-order, invariant domain preserving, guaranteed maximum speed method using a graph viscosity (GMS-GV1) with an invariant domain violating, but entropy consistent, high-order method. Invariant domain preserving auxiliary states, naturally produced by the GMS-GV1 method, are used to define local bounds for the high-order method, which is then made invariant domain preserving via a convex limiting process. Numerical tests confirm the second-order accuracy of the new GMS-GV2 method in the maximum norm, where the 2 stands for second-order. The proposed convex limiting is generic and can be applied to other approximation techniques and other hyperbolic systems.
|
|
3. |
- Lu, Li, et al.
(författare)
-
Nonlinear artificial viscosity for spectral element methods
- 2019
-
Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 357:7, s. 646-654
-
Tidskriftsartikel (refereegranskat)abstract
- We present a filter-based approach to computing artificial viscosities for spectral element methods. A number of applications for this approach are presented.
|
|
4. |
|
|
5. |
|
|
6. |
|
|