A deformable particle-in-cell method for advective transport in geodynamic modelling
Résumé
This paper presents an improvement of the particle-in-cell (PIC) method commonly used in geodynamic modelling for solving pure advection of sharply varying fields. Standard PIC approaches use particle kernels to transfer the information carried by the Lagrangian particles to/from the Eulerian grid. These kernels are generally 1-D and non-evolutive, which leads to the development of under- and oversampling of the spatial domain by the particles. This reduces the accuracy of the solution, and may require the use of a prohibitive amount of particles in order to maintain the solution accuracy to an acceptable level. The new proposed approach relies on the use of deformable kernels that account for the strain history in the vicinity of particles. It results in a significant improvement of the spatial sampling by the particles, leading to a much higher accuracy of the numerical solution, for a reasonable computational extra cost. Various 2-D tests were conducted to compare the performances of the deformable PIC (DPIC) method with the PIC approach. These consistently show that at comparable accuracy, the DPIC method was found to be four to six times more efficient than standard PIC approaches. The method could be adapted to 3-D space and generalized to cases including motionless transport.
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