Please cite this article in press as: A. Nejadmalayeri et al., Parallel adaptive wavelet collocation method for PDEs, J. Comput. Phys. (2015), http://dx.
AbstractA parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogenous turbulence with linear forcing at effective non-adaptive resolutions up to 2048 3 using as many as 2048 CPU cores.
The recent development of the adaptive-anisotropic wavelet-collocation method, which incorporates the use of coordinate transforms, opens new horizons for wavelet-based simulations of wall-bounded turbulent flows. The new wavelet-based adaptive unsteady Reynolds-averaged Navier–Stokes approach for computational modelling of turbulent flows is presented. The proposed methodology that is integrated with anisotropic wavelet-based mesh refinement is demonstrated for a two-equation eddy-viscosity turbulence model. The performance of the method is assessed by conducting numerical simulations of the turbulent flow past a circular cylinder at subcritical Reynolds number. The present study demonstrates both the feasibility and the effectiveness of the new wavelet-based adaptive unsteady Reynolds-averaged turbulence modelling procedure for external flows.
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