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Editorial: Preface to the special issue “Recent advances in numerical methods for hyperbolic partial differential equations”. (English) Zbl 1409.00105

This special issue is dedicated to recent advances in numerical methods for such nonlinear systems of hyperbolic PDE and tries to cover a wide spectrum of different problems and numerical approaches.
The papers of this special issue cover the following sub-topics in the field of numerical methods for nonlinear hyperbolic PDE:
Novel Riemann solvers for complex hyperbolic PDE
Hyperbolic PDE with involutions, concerning also the divergence constraint in the Maxwell and MHD equations
Efficient high order methods with adaptive mesh refinement (AMR)
Discontinuous Galerkin finite element methods
Computational hemodynamics
Discretization of Friedrichs systems
Multi-phase flows
Hyperbolic PDE with higher order derivatives
Compressible Navier-Stokes equations

MSC:

00B15 Collections of articles of miscellaneous specific interest
76-06 Proceedings, conferences, collections, etc. pertaining to fluid mechanics
65-06 Proceedings, conferences, collections, etc. pertaining to numerical analysis

Biographic References:

Munz, Claus-Dieter

Software:

FS3D
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Castro, M. J.; Gallardo, J. M.; Marquina, A., Approximate Osher-Solomon schemes for hyperbolic systems, Applied Mathematics and Computation (2015) · Zbl 1402.35019
[2] Sánchez-Linares, C.; Morales de Luna, T.; Castro Díaz, M. J., A HLLC scheme for Ripa model, Applied Mathematics and Computation (2015) · Zbl 1410.76261
[3] Betancourt, F.; Rohde, C., Finite-volume schemes for Friedrichs systems with involutions, Applied Mathematics and Computation (2015)
[4] Campos Pinto, M.; Mounier, M.; Sonnendrücker, E., Handling the divergence constraints in Maxwell and Vlasov-Maxwell simulations, Applied Mathematics and Computation (2015) · Zbl 1410.82027
[5] Kemm, F., Roe-type schemes for shallow water magnetohydrodynamics with hyperbolic divergence cleaning, Applied Mathematics and Computation (2015) · Zbl 1410.76238
[6] Buchmüller, P.; Dreher, J.; Helzel, C., Finite volume WENO methods for hyperbolic conservation laws on Cartesian grids with adaptive mesh refinement, Applied Mathematics and Computation (2015)
[8] Dumbser, M.; Facchini, M., A space-time discontinuous Galerkin method for Boussinesq-type equations, Applied Mathematics and Computation (2015) · Zbl 1410.76167
[9] Gassner, G. J.; Winters, A. R.; Kopriva, D. A., A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations, Applied Mathematics and Computation (2015) · Zbl 1410.65393
[10] Kopriva, D. A.; Gassner, G. J., Geometry effects in nodal discontinuous Galerkin methods on curved elements that are provably stable, Applied Mathematics and Computation (2015) · Zbl 1410.65372
[12] Wang, H.; Shu, C. W.; Zhang, Q., Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for nonlinear convection-diffusion problems, Applied Mathematics and Computation (2015)
[13] Toro, E. F., Brain venous haemodynamics, neurological diseases and mathematical modelling. A review, Applied Mathematics and Computation (2015) · Zbl 1410.76487
[14] Després, B.; Buet, C., The structure of well-balanced schemes for Friedrichs systems with linear relaxation, Applied Mathematics and Computation (2015)
[15] Eisenschmidt, K.; Ertl, M.; Gomaa, H.; Kieffer-Roth, C.; Meister, C.; Rauschenberger, P.; Reitzle, M.; Schlottke, K.; Weigand, B., Direct numerical simulations for multiphase flows: An overview of the multiphase code FS3D, Applied Mathematics and Computation (2015) · Zbl 1410.76004
[16] Furfaro, D.; Saurel, R., Modeling droplet phase change in the presence of a multi-component gas mixture, Applied Mathematics and Computation (2015)
[17] Dumbser, M.; Casulli, V., A conservative, weakly nonlinear semi-implicit finite volume scheme for the compressible Navier-Stokes equations with general equation of state, Applied Mathematics and Computation (2015)
[18] Meysonnat, P. S.; Koh, S. R.; Roidl, B.; Schröder, W., Impact of transversal traveling surface waves in a non-zero pressure gradient turbulent boundary layer flow, Applied Mathematics and Computation (2015)
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