19 research outputs found

    Parallel Algorithms for Semi-Lagrangian Advection

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    Numerical time-step limitations associated with the explicit treatment of advection-dominated problems in computational fluid dynamics are often relaxed by employing Eulerian-Lagrangian methods. These are also known as semi-Lagrangian methods in the atmospheric sciences. Such methods involve backward time integration of a characteristic equation to find the departure point of a fluid particle arriving at an Eulerian grid point. The value of an advected field at the departure point is obtained by interpolation. Both the trajectory integration and repeated interpolation influence accuracy. We compare the accuracy and performance of interpolation schemes based on piecewise cubic polynomials and cubic B-splines in the context of a distributed-memory, parallel computing environment. The computational cost and inter-processor communication requirements for both methods are reported. Spline interpolation has better conservation properties but requires the solution of a global linear system, i..

    A New Dynamics Kernel For The MC2 Model II: Flexible GMRES Elliptic Solver

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    The Mesoscale Compressible Community (MC2) model is an extension of a fully compressible limited area model developed by Monique Tanguay, Andre Robert and Rene Laprise in the mid-1980's. The model employs a three-time-level semi-implicit, semi-Lagrangian time discretisation with modified terrain following Gal-Chen coordinates. The semi-implicit scheme results in an elliptic boundary value problem with first-order derivative terms in the vertical direction and thus the resulting discretised system of equations has a large sparse nonsymmetric coefficient matrix. To build a massively parallel implemenation of the model, the original alternating direction implicit (ADI) elliptic solver has been replaced with a flexible Generalised Minimum Residual (GMRES) Krylov method with variable preconditioning. We report on the performance of successive over relaxation (SOR) and vertical line relaxation (ADI) as preconditioners to improve the convergence rate of GMRES. A meteorological comparison base..

    Shared And Distributed Memory Implementations Of The Canadian MC2 Model

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    The Mesoscale Compressible Community (MC2) model is an extension of a fully compressible limited area model developed by Monique Tanguay, Andre Robert and Rene Laprise in the mid-1980's. The model employs a three-timelevel semi-implicit, semi-Lagrangian time discretisation with modified terrain following Gal-Chen coordinates. The semi-implicit scheme results in an elliptic boundary value problem with first-order derivative terms in the vertical direction and thus the resulting discretised system of equations has a large sparse nonsymmetric coefficient matrix. The original alternating direction implicit (ADI) elliptic solver has been replaced with a flexible Generalised Minimum Residual (GMRES) Krylov method with variable preconditioning. We report on the performance of successive over relaxation (SOR) and vertical line relaxation (ADI) as parallel preconditioners to improve the convergence rate of GMRES. Parallelisation of the model for a distributed-memory computing environment has be..
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