Name
Abstract | ||
|---|---|---|
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.jcp.2010.04.013 | J. Comput. Physics |
Keywords | Field | DocType |
compressible ideal mhd equation,numerical formulation,compressible flow,fifth-order accurate finite difference,magnetohydrodynamics,smooth extremum,glm-mhd scheme,cell-centered mhd,high-order conservative finite difference,monotonicity preserving,proposed numerical method,different reconstruction technique,cell-centered methods,extensive numerical testing,smooth region,weno schemes,mhd equation,higher-order methods,numerical solution,lagrange multiplier,numerical method,cost effectiveness,finite difference | Discretization,Mathematical optimization,Polynomial,Lagrange multiplier,Finite difference,Mathematical analysis,Discontinuity (linguistics),Robustness (computer science),Numerical analysis,Mathematics,Parabola | Journal |
Volume | Issue | ISSN |
229 | 17 | Journal of Computational Physics |
Citations | PageRank | References |
18 | 1.01 | 20 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrea Mignone | 1 | 36 | 4.45 |
| petros tzeferacos | 2 | 39 | 4.74 |
| Gianluigi Bodo | 3 | 18 | 1.01 |