New Types of Jacobian-Free Approximate Riemann Solvers for Hyperbolic Systems

2017 ◽  
pp. 23-31
Author(s):  
Manuel J. Castro ◽  
José M. Gallardo ◽  
Antonio Marquina
Keyword(s):  
Hyperbolic Systems ◽  
Riemann Solvers ◽  
Approximate Riemann Solvers

A REDUCED STABILITY CONDITION FOR NONLINEAR RELAXATION TO CONSERVATION LAWS

2004 ◽  
Vol 01 (01) ◽  
pp. 149-170 ◽  
Author(s):  
FRANÇOIS BOUCHUT
Keyword(s):  
Conservation Laws ◽  
Stability Condition ◽  
Hyperbolic Systems ◽  
Strong Stability ◽  
Riemann Solvers ◽  
Systems Of Conservation Laws ◽  
Leading Term ◽  
Relaxation Systems ◽  
The One ◽  
Approximate Riemann Solvers

We consider multidimensional hyperbolic systems of conservation laws with relaxation, together with their associated limit systems. A strong stability condition for such asymptotics has been introduced by Chen, Levermore and Liu, namely the existence of an entropy extension. We propose here a new stability condition, the reduced stability condition, which is weaker than the previous one, but still has the property to imply the subcharacteristic or interlacing conditions, and the dissipativity of the leading term in the Chapman–Enskog expansion. This reduced stability condition has the advantage of involving only the submanifold of equilibria, or maxwellians, so that it is much easier to check than the entropy extension condition. Our condition generalizes the one introduced by the author in the case of kinetic, i.e. diagonal semilinear relaxation. We provide an adapted stability analysis in the context of approximate Riemann solvers obtained via relaxation systems.

Approximate Riemann solvers for the Godunov SPH (GSPH)

2014 ◽  
Vol 270 ◽  
pp. 432-458 ◽  
Author(s):  
Kunal Puri ◽  
Prabhu Ramachandran
Keyword(s):  
Riemann Solvers ◽  
Approximate Riemann Solvers

AUSM-Based High-Order Solution for Euler Equations

2012 ◽  
Vol 12 (4) ◽  
pp. 1096-1120 ◽  
Author(s):  
Angelo L. Scandaliato ◽  
Meng-Sing Liou
Keyword(s):  
Euler Equations ◽  
Splitting Method ◽  
High Order ◽  
Riemann Solvers ◽  
Carbuncle Phenomenon ◽  
Solution Accuracy ◽  
Matrix Vector ◽  
Approximate Riemann Solvers ◽  
Monotonicity Preserving ◽  
High Order Interpolation

AbstractIn this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method (AUSM), specifically AUSM+-UP, with high-order upwind-biased interpolation procedures, the weighted essentially non-oscillatory (WENO-JS) scheme and its variations, and the monotonicity preserving (MP) scheme, for solving the Euler equations. MP is found to be more effective than the three WENO variations studied. AUSM+-UP is also shown to be free of the so-called “carbuncle” phenomenon with the high-order interpolation. The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables, even though they require additional matrix-vector operations. Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison. In addition, four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy. Finally, a measure for quantifying the efficiency of obtaining high order solutions is proposed; the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.

scholarly journals On a class of genuinely 2D incomplete Riemann solvers for hyperbolic systems

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
José M. Gallardo ◽  
Kleiton A. Schneider ◽  
Manuel J. Castro
Keyword(s):  
Hyperbolic Systems ◽  
Riemann Solvers

Exact and approximate Riemann solvers at phase boundaries

2013 ◽  
Vol 75 ◽  
pp. 112-126 ◽  
Author(s):  
S. Fechter ◽  
F. Jaegle ◽  
V. Schleper
Keyword(s):  
Phase Boundaries ◽  
Riemann Solvers ◽  
Approximate Riemann Solvers
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