Browsing by Author "Clain, S."
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- Comparison between MUSCL and MOOD techniques in a finite volume well-balanced code to solve SWE. The Tohoku-Oki, 2011 examplePublication . Reis, C.; Figueiredo, J.; Clain, S.; Omira, R.; Baptista, Maria Ana Carvalho Viana; MIRANDA, JORGE MIGUELNumerical 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.
- Second-order finite volume with hydrostatic reconstruction for tsunami simulationPublication . Clain, S.; Reis, C.; Costa, R.; Figueiredo, J.; Baptista, Maria Ana Carvalho Viana; Miranda, Jorge MiguelTsunami modeling commonly accepts the shallow water system as governing equations where the major difficulty is the correct treatment of the nonconservative term due to bathymetry variations. The finite volume method for solving the shallow water equations with such source terms has received great attention in the two last decades. The built-in conservation property, the capacity to correctly treat discontinuities, and the ability to handle complex bathymetry configurations preserving some steady state configurations (well-balanced scheme) make the method very efficient. Nevertheless, it is still a challenge to build an efficient numerical scheme, with very few numerical artifacts (e. g., small numerical diffusion, correct propagation of the discontinuities, accuracy, and robustness), to be used in an operational environment, and that is able to better capture the dynamics of the wet-dry interface and the physical phenomena that occur in the inundation area. In the first part of this paper, we present a new second-order finite volume code. The code is developed for the shallow water equations with a nonconservative term based on the hydrostatic reconstruction technology to achieve a well-balanced scheme and an adequate dry/wet interface treatment. A detailed presentation of the numerical method is given. In the second part of the paper, we highlight the advantages of the new numerical technique. We benchmark the numerical code against analytical, experimental, and field results to assess the robustness and the accuracy of the numerical code. Finally, we use the 28 February 1969 North East Atlantic tsunami to check the performance of the code with real data.