0000000000074023
AUTHOR
José M. Gallardo
showing 5 related works from this author
New Types of Jacobian-Free Approximate Riemann Solvers for Hyperbolic Systems
2017
We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Moreover, they can be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems with complex Jacobians, as the relativistic magnetohydrodynamics (RMHD) equations. The proposed solvers have also been extended to the case of approximate DOT (Dumbser-Osher-Toro) methods, which can be regarded as simple and efficient approximations to the classical Osher-Solomon method. Som…
Jacobian-Free Incomplete Riemann Solvers
2018
The purpose of this work is to present some recent developments about incomplete Riemann solvers for general hyperbolic systems. Polynomial Viscosity Matrix (PVM) methods based on internal approximations to the absolute value function are introduced, and they are compared with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Moreover, they can be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions. Some numerical experiments involving the relativistic magnetohydrodyn…
Incomplete Riemann Solvers Based on Functional Approximations to the Absolute Value Function
2021
We give an overview on the work developed in recent years about certain classes of incomplete Riemann solvers for hyperbolic systems. These solvers are based on polynomial or rational approximations to |x|, and they do not require the knowledge of the complete eigenstructure of the system, but only a bound on the maximum wave speed. Our solvers can be readily applied to nonconservative hyperbolic systems, by following the theory of path-conservative schemes. In particular, this allows for an automatic treatment of source or coupling terms in systems of balance laws. The properties of our schemes have been tested with some challenging numerical experiments involving systems such as the Euler…
Approximate Osher–Solomon schemes for hyperbolic systems
2016
This paper is concerned with a new kind of Riemann solvers for hyperbolic systems, which can be applied both in the conservative and nonconservative cases. In particular, the proposed schemes constitute a simple version of the classical Osher-Solomon Riemann solver, and extend in some sense the schemes proposed in Dumbser and Toro (2011) 19,20. The viscosity matrix of the numerical flux is constructed as a linear combination of functional evaluations of the Jacobian of the flux at several quadrature points. Some families of functions have been proposed to this end: Chebyshev polynomials and rational-type functions. Our schemes have been tested with different initial value Riemann problems f…
Jacobian-free approximate solvers for hyperbolic systems: Application to relativistic magnetohydrodynamics
2017
Abstract We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function, and compare them with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Another important feature of the proposed methods is that they are suitable to be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions, e.g., the relativistic magnetohydrodynamics (RMHD) equations. On the other hand, the proposed Jacobian-free solvers hav…