Comparison between MUSCL and MOOD techniques in a finite volume well-balanced code to solve SWE. The Tohoku-Oki, 2011 example

Abstract

Numerical modelling is a fundamental tool for scenario-based evaluation of hazardous phenomena such as tsunami. Nevertheless, the numerical prediction highly depends on the tool quality and therefore the design of efficient numerical schemes that provide robust and accurate solutions still receives considerable attention. In this paper, we implement two different second-order finite volume numerical schemes deriving from an a priori or an a posteriori limitation procedure and we compare their efficiency in solving the non-conservative shallow-water equations. The numerical schemes assessed here are two variants of the a priori Monotonic Upstream-Centred Scheme for Conservation Laws (MUSCL) and the recent a posteriori multidimensional optimal order detection (MOOD) technique. We benchmark the numerical code, equipped with MUSCL and MOOD techniques, against: (1) a 1-D stationary problem with non-constant bathymetry to assess the second-order convergence of the method when a smooth analytical solution is involved; (2) a 1-D dam-break test to show its capacity to deal with irregular and discontinuous bathymetry in wet zones; and (3) using a simple 1-D analytical tsunami benchmark, ‘single wave on a sloping beach’, we show that the classical 1-D shallow-water system can be accurately solved by the second-order finite volume methods. Furthermore, we test the performance of the numerical code for the real-case tsunami of Tohoku-Oki, 2011. Through a set of 2-D numerical simulations, the 2011 tsunami records from both DART and GPS buoys are checked against the simulated results using MUSCL and MOOD.We find that the use of the MOOD technique leads to a better approximation between the numerical solutions and the observations than the MUSCL one. MOOD allows sharper shock capture and generates less numerical diffusion, suggesting it as a promising technique for solving shallow-water problems.