Séance Séminaire

Séminaire ACSIOM

A modified parareal method for solving the two-dimensional nonlinear shallow water equations

Parareal methods have been developed over the past two decades as an approach for reducing the computational time required for the simulation of fine, accurate models. Its main idea consists in parallelizing in time a fine simulation by using alongside a coarser and less expensive model, in a predictor-corrector iterative procedure. Although very efficient in several applications, the parareal method, in its original formulation, presents instabilities and/or slow convergence for hyperbolic or advection-dominated problems. Adaptations of the method for treating them introduce reduced-order models (ROMs) in the parareal iterations, using the snapshot-POD-DEIM (proper orthogonal decomposition - discrete empirical interpolation method) procedure. In this work, we solve the two-dimensional nonlinear shallow water equations using the ROM-based parareal algorithm. We also propose a modification of the method for further stability and convergence improvements, by enriching the snapshots sets used in the POD-DEIM with no additional cost for computing the extra snapshots. Numerical tests are performed for comparing the performance of the original parareal method, the ROM-based one and our proposed modification.

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