In this paper, we present an exact Riemann solver for one-dimensional systems of conservation laws. The method is based on an offline-online computational decomposition. During the offline stage, we generate an accurate surrogate model for the solution to the Riemann problem for arbitrary left and right states. Then, during the online stage, we employ the surrogate model to generate accurate initial conditions for an iterative Newton solver. We present a mathematical analysis of the Riemann problem to justify the proposed approach. Finally, we illustrate its effectiveness by means of two numerical examples.
An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws / Taddei, T; Quarteroni, A; Salsa, S. - In: VIETNAM JOURNAL OF MATHEMATICS. - ISSN 2305-2228. - 42:2(2016), pp. 214-243. [10.1007/s10013-016-0212-0]
An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws
Taddei T
;
2016
Abstract
In this paper, we present an exact Riemann solver for one-dimensional systems of conservation laws. The method is based on an offline-online computational decomposition. During the offline stage, we generate an accurate surrogate model for the solution to the Riemann problem for arbitrary left and right states. Then, during the online stage, we employ the surrogate model to generate accurate initial conditions for an iterative Newton solver. We present a mathematical analysis of the Riemann problem to justify the proposed approach. Finally, we illustrate its effectiveness by means of two numerical examples.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
