Abstract
This paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed algorithm of the solution minimizes the numerical errors and is unconditionally stable. Consequently, it is possible to perform computations with a significantly greater time step than in the case of the explicit scheme. An additional efficiency improvement was achieved using the symmetry of the tridiagonal matrix of the arising system of nonlinear equations, due to the application of the parallelization strategy. The computational experiments showed that the proposed parallel implementation of the implicit scheme is very effective, at about two orders of magnitude with regard to computational time, in comparison with the explicit one.
Highlights
In river valleys protected by embankments, floods can occur in adjacent areas due to a dike break or during controlled inflows of flood water into polders
This paper focuses on two main aspects of the solution of a 2D diffusive wave equation for floodplain inundation problems
In the case of an implicit scheme, the accuracy of the calculations depends on the value of the weighting parameter θ and the time step
Summary
In river valleys protected by embankments, floods can occur in adjacent areas due to a dike break or during controlled inflows of flood water into polders. Apart from the accuracy and stability of the applied numerical scheme, an important problem is the computational efficiency, which can be defined as the number of arithmetic operations carried out at a certain time in order to obtain a numerical solution with assumed accuracy This issue deserves special attention in terms of simulating real scenarios for unsteady flows over vast floodplains. The first concerns improvements for efficiency of the numerical solution, by concentrating on the use of the implicit scheme in parallel computations For this purpose, in the proposed algorithm, a high computational efficiency was achieved by the application of the dimensional splitting technique and the implicit time integration scheme, which is unconditionally stable, as well as the modified Picard method for the solution of the nonlinear systems of equations, which ensures convergent iterations. The second aspect relates to comparing the computational efficiency as well as accuracy of the proposed method with the commonly used algorithm based on the explicit scheme
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