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Computational study demonstrates efficient parallel scalar advection coupling finite element fluid solvers with semi-Lagrangian particles, indicating high performance on distributed supercomputers.
This paper focuses on the development and application of a parallel implementation of a hybrid numerical method. It combines a mesh-based approach-specifically, the Finite Element Method (FEM)–for solving the Navier-Stokes equations, with a semi-Lagrangian particle method for the advection-diffusion of a scalar function. Both methods are implemented in parallel on distributed-memory supercomputers and are coupled in a one-way fashion, where the velocity field from the mesh-based solver feeds into the semi-Lagrangian solver. Parallelisation of the solvers and their coupling is achieved using the MPI library. Special attention is paid to the efficiency of the implementation. Computational performance is enhanced through the integration of an external library that minimises the busy-waiting behaviour of MPI subroutines during data exchange, ensuring optimal utilisation of available computational resources. Finally, the method is applied to simulate the advection of a high-Schmidt-number scalar in a jet flow, demonstrating its effectiveness and performance.
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Santoso et al. (2026) studied this question.
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