We present a semi-analytical, implicit solution to the generalized Riemann problem (GRP) for non-linear systems of hyperbolic balance laws with stiff source terms. The solution method is based on an implicit, time Taylor series expansion and the Cauchy-Kowalewskaya procedure, along with the solution of a sequence of classical Riemann problems. Our new GRP solver is then used to construct locally implicit ADER methods of arbitrary accuracy in space and time for solving the general initial-boundary value problem for non-linear systems of hyperbolic balance laws with stiff source terms. Analysis of the method for model problems is carried out and empirical convergence rate studies for suitable tests problems are performed, confirming the theoretically expected high order of accuracy.

Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws / Toro, E. F.; Montecinos, G. I.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 303:(2015), pp. 146-172. [10.1016/j.jcp.2015.09.039]

Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws

Toro E. F.;
2015-01-01

Abstract

We present a semi-analytical, implicit solution to the generalized Riemann problem (GRP) for non-linear systems of hyperbolic balance laws with stiff source terms. The solution method is based on an implicit, time Taylor series expansion and the Cauchy-Kowalewskaya procedure, along with the solution of a sequence of classical Riemann problems. Our new GRP solver is then used to construct locally implicit ADER methods of arbitrary accuracy in space and time for solving the general initial-boundary value problem for non-linear systems of hyperbolic balance laws with stiff source terms. Analysis of the method for model problems is carried out and empirical convergence rate studies for suitable tests problems are performed, confirming the theoretically expected high order of accuracy.
2015
Toro, E. F.; Montecinos, G. I.
Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws / Toro, E. F.; Montecinos, G. I.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 303:(2015), pp. 146-172. [10.1016/j.jcp.2015.09.039]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/332149
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