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M. Sekhar

Publications and source records attributed to M. Sekhar.

3 recordsLinked to original sources

An open source massively parallel solver for Richards equation: Mechanistic modelling of water fluxes at the watershed scale

In this paper we present a massively parallel open source solver for Richards equation, named the RichardsFOAM solver. This solver has been developed in the framework of the open source generalist computational fluid dynamics tool box OpenFOAM (R) and is capable to deal with large scale problems in both space and time. The source code for RichardsFOAM may be downloaded from the CPC program library website.It exhibits good parallel performances (up to $\sim$90% parallel efficiency with 1024 processors both in strong and weak scaling), and the conditions required for obtaining such performances are analysed and discussed. These performances enable the mechanistic modelling of water fluxes at the scale of experimental watersheds (up to few square kilometres of surface area), and on time scales of decades to a century. Such a solver can be useful in various applications, such as environmental engineering for long term transport of pollutants in soils, water engineering for assessing the impact of land settlement on water resources, or in the study of weathering processes on the watersheds.

cs.CE

An upwind method for genuine weakly hyperbolic systems

In this article, we attempted to develop an upwind scheme based on Flux Difference Splitting using Jordan canonical forms to simulate genuine weakly hyperbolic systems. Theory of Jordan Canonical Forms is being used to complete defective set of linear independent eigenvectors. Proposed FDS-J scheme is capable of recognizing various shocks accurately.

math.NA

Use of Jordan forms for convection-pressure split Euler solvers

In this study, we analyze convection-pressure split Euler flux functions which contain genuine weakly hyperbolic convection subsystems. A system is said to be a genuine weakly hyperbolic if all eigenvalues are real with no complete set of linearly independent (LI) eigenvectors. To construct an upwind solver based on flux difference splitting (FDS) framework, we require to generate complete set of LI eigenvectors. This can be done through addition of generalized eigenvectors which can be computed from theory of Jordan canonical forms. Once we have complete set of LI generalized eigenvectors, we construct upwind solvers in convection-pressure splitting framework. Since generalized eigenvectors are not unique, we take extra care to ensure no direct contribution of generalized eigenvectors in the final formulation of both the newly developed numerical schemes. First scheme is based on Zha and Bilgen type splitting approach, while second is based on Toro and V\'azquez splitting. Both the schemes are tested on several bench-mark test problems on 1-D and one of them is tested on some typical 2-D test problems which involve shock instabilities. The concept of generalized eigenvector based on Jordan forms is found to be useful in dealing with the genuine weakly hyperbolic parts of the considered Euler systems.

math.NA