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Abstract
This paper shows an application of a vertex-based Compatible Discrete Operator (CDO) scheme to simulate the Richards equation on meshes using polyhedral cells. Second order spatial accuracy is reached for a verification test case using two meshes made of different types of polyhedral cells. A second validation test case dealing with a variably saturated soil inside a vertical column has been simulated, with three advected passive pollutants being released. Results are in good agreement with the reference for both types of mesh. MPI scalability has also been assessed at scale up to 98,304 cores of a Cray X30 for a 1.7 B cell mesh for the simulation of the aforementioned case, and nearly linear speed-up is observed. Finally the implementation of hybrid MPI-OpenMP has been tested on 2 types of Intel Xeon Phi Knights Landing co-processors, showing that the best configuration for the code is obtained when all the physical cores are filled by MPI tasks and the 4 hyperthreads by OpenMP threads.
Highlights
Advances in Computational Fluid Dynamics (CFD), multi-physics, numerical schemes, and High Performance Computing (HPC) make it possible to envisage extremely large simulations to model complex processes in complex configurations
A way to reduce these back and forth iterations is to switch from the traditional Finite Volume (FV) [1] and Finite Element (FE) [2] approaches to methods which are more robust and more flexible while keeping a high accuracy
A side effect of this flexibility is the addition of polyhedral cells at the interface between the two meshes to join if this interface is non-conforming
Summary
Advances in Computational Fluid Dynamics (CFD), multi-physics, numerical schemes, and High Performance Computing (HPC) make it possible to envisage extremely large simulations to model complex processes in complex configurations. Creating a mesh suitable for these complex geometries which will produce accurate results might take more than 80% of the duration of a project, as many back and forth iterations between mesh generation and solver testing are required to derive the optimal input parameters for the solver. Several schemes sharing similar principles with the CDO schemes have been proposed, e.g. Mimetic Finite Differences [14, 15], Discrete Geometric Approach [16], Vertex Approximate Gradient scheme [17], SUSHI scheme [18] All these schemes can be recast into the generic mathematical framework called Gradient schemes [19]. The ambition of this work and its novelty is to retain this level of parallelisation with the newly implemented CDO schemes, and to develop an hybrid MPI-OpenMP software showing good performance at scale, when keeping spacial second order accuracy for polyhedral cell meshes.
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