Alireza Nejadmalayeri

Parallel adaptive wavelet collocation method for PDEs

A 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 homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 20483 using as many as 2048 CPU cores.

Reynolds number scaling of coherent vortex simulation and stochastic coherent adaptive large eddy simulation

In view of the ongoing longtime pursuit of numerical approaches that can capture important flow physics of high Reynolds number flows with fewest degrees of freedom, two important wavelet-based multi-resolution schemes are thoroughly examined, namely, the Coherent Vortex Simulation (CVS) and the Stochastic Coherent Adaptive Large Eddy Simulation (SCALES) with constant and spatially/temporarily variable thresholding. Reynolds number scaling of active spatial modes for CVS and SCALES of linearly forced homogeneous turbulence at high Reynolds numbers is investigated in dynamic study for the first time. This dynamic computational complexity study demonstrates that wavelet-based methods can capture flow-physics while using substantially fewer degrees of freedom than both direct numerical simulation and marginally resolved LES with the same level of fidelity or turbulence resolution, defined as ratio of subgrid scale and the total dissipations. The study provides four important observations: (1) the linear Reyn...

Spatially Variable Thresholding for Stochastic Coherent Adaptive LES

The properties of wavelet transform, viz. the ability to identify and efficiently represent temporal/spatial coherent flow structures, self-adaptiveness, and de-noising, have made them attractive candidates for constructing multi-resolution variable fidelity schemes for simulations of turbulence (Schneider and Vasilyev, 2010). Stochastic Coherent Adaptive Large Eddy Simulation (SCALES) (Goldstein and Vasilyev, 2004) is the most recent wavelet-based methodology for numerical simulations of turbulent flows that resolves energy containing turbulent motions using wavelet multi-resolution decomposition and self-adaptivity. In this technique, the extraction of the most energetic structures is achieved using wavelet thresholding filter with a priori prescribed threshold level.

Adaptive LES of Immersed-Body Flows Based on Variable Wavelet Threshold Filtering

In the wavelet-based adaptive large-eddy simulation (LES) approach to turbulent flows, the multi-resolution wavelet threshold filtering (WTF) procedure is exploited to separate coherent energetic eddies, which are resolved, from residual background flow, which is modeled.

Computational Complexity of Adaptive LES with Variable Fidelity Model Refinement

Adaptive methods with both mesh and polynomial order refinements have been used extensively in computational fluid dynamics to achieve optimal accuracy with the minimal computational cost.