scholarly journals Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers

2015 ◽  
Vol 299 ◽  
pp. 687-715 ◽  
Author(s):  
Dinshaw S. Balsara ◽  
Michael Dumbser
Keyword(s):  
Finite Volume ◽  
Unstructured Meshes ◽  
High Order ◽  
Finite Volume Schemes ◽  
Riemann Solvers ◽  
Divergence Free

scholarly journals Approximate Riemann Solvers and Robust High-Order Finite Volume Schemes for Multi-Dimensional Ideal MHD Equations

2011 ◽  
Vol 9 (2) ◽  
pp. 324-362 ◽  
Author(s):  
Franz Georg Fuchs ◽  
Andrew D. McMurry ◽  
Siddhartha Mishra ◽  
Nils Henrik Risebro ◽  
Knut Waagan
Keyword(s):  
Finite Volume ◽  
Source Term ◽  
Second Order ◽  
High Order ◽  
Mhd Equations ◽  
Positive Pressure ◽  
Finite Volume Schemes ◽  
Riemann Solvers ◽  
Ideal Mhd ◽  
Approximate Riemann Solvers

AbstractWe design stable and high-order accurate finite volume schemes for the ideal MHD equations in multi-dimensions. We obtain excellent numerical stability due to some new elements in the algorithm. The schemes are based on three- and five-wave approximate Riemann solvers of the HLL-type, with the novelty that we allow a varying normal magnetic field. This is achieved by considering the semi-conservative Godunov-Powell form of the MHD equations. We show that it is important to discretize the Godunov-Powell source term in the right way, and that the HLL-type solvers naturally provide a stable upwind discretization. Second-order versions of the ENO- and WENO-type reconstructions are proposed, together with precise modifications necessary to preserve positive pressure and density. Extending the discrete source term to second order while maintaining stability requires non-standard techniques, which we present. The first- and second-order schemes are tested on a suite of numerical experiments demonstrating impressive numerical resolution as well as stability, even on very fine meshes.

ENHANCING IMPLICIT HIGH-ORDER SPECTRAL FINITE VOLUME SCHEMES APPLICABILITY ON UNSTRUCTURED MESHES

2015 ◽  
Author(s):  
Fernanda Paula Barbosa Pola ◽  
Ives Renê Venturini Pola ◽  
Antonio Castelo Filho
Keyword(s):  
Finite Volume ◽  
Unstructured Meshes ◽  
High Order ◽  
Finite Volume Schemes
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