An open and parallel multiresolution framework using block-based adaptive grids

A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and explicit time integration. Grid refinement and coarsening are triggered by multiresolution analysis, i.e. thresholding of wavelet coefficients, which allow controlling the precision of the adaptive approximation of the solution with respect to uniform grid computations. The implementation of the scheme is fully parallel using MPI with a hybrid data structure. Load balancing relies on space filling curves techniques. Validation tests for 2D advection equations allow to assess the precision and performance of the developed code. Computations of the compressible Navier-Stokes equations for a temporally developing 2D mixing layer illustrate the properties of the code for nonlinear multi-scale problems. The code is open source

Achieving High Speed CFD simulations: Optimization, Parallelization, and FPGA Acceleration for the unstructured DLR TAU Code

Today, large scale parallel simulations are fundamental tools to handle complex problems. The number of processors in current computation platforms has been recently increased and therefore it is necessary to optimize the application performance and to enhance the scalability of massively-parallel systems. In addition, new heterogeneous architectures, combining conventional processors with specific hardware, like FPGAs, to accelerate the most time consuming functions are considered as a strong alternative to boost the performance. In this paper, the performance of the DLR TAU code is analyzed and optimized. The improvement of the code efficiency is addressed through three key activities: Optimization, parallelization and hardware acceleration. At first, a profiling analysis of the most time-consuming processes of the Reynolds Averaged Navier Stokes flow solver on a three-dimensional unstructured mesh is performed. Then, a study of the code scalability with new partitioning algorithms are tested to show the most suitable partitioning algorithms for the selected applications. Finally, a feasibility study on the application of FPGAs and GPUs for the hardware acceleration of CFD simulations is presented

Finite element methods for deterministic simulation of polymeric fluids

In this work we consider a finite element method for solving the coupled Navier-Stokes (NS) and Fokker-Planck (FP) multiscale model that describes the dynamics of dilute polymeric fluids. Deterministic approaches such as ours have not received much attention in the literature because they present a formidable computational challenge, due to the fact that the analytical solution to the Fokker-Planck equation may be a function of a large number of independent variables. For instance, to simulate a non-homogeneous flow one must solve the coupled NS-FP system in which (for a 3-dimensional flow, using the dumbbell model for polymers) the Fokker-Planck equation is posed in a 6-dimensional domain. In this work we seek to demonstrate the feasibility of our deterministic approach. We begin by discussing the physical and mathematical foundations of the NS-FP model. We then present a literature review of relevant developments in computational rheology and develop our deterministic finite element based method in detail. Numerical results demonstrating the efficiency of our approach are then given, including some novel results for the simulation of a fully 3-dimensional flow. We utilise parallel computation to perform the large-scale numerical simulations

An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver

We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the pseudo-compressibility method recently proposed by Guermond and Minev [Comptes Rendus Mathematique, 348:581-585, 2010] that uses a directional splitting strategy to discretize the incompressible Navier-Stokes equations, thereby reducing the linear systems to a series of one-dimensional tridiagonal systems. We perform numerical simulations of several fluid-structure interaction problems in two and three dimensions and study the accuracy and convergence rates of the proposed algorithm. For these problems, we compare the proposed algorithm against other second-order projection-based fluid solvers. Lastly, the strong and weak scaling properties of the proposed algorithm are investigated

A Test Suite for High-Performance Parallel Java

The Java programming language has a number of features that make it attractive for writing high-quality, portable parallel programs. A pure object formulation, strong typing and the exception model make programs easier to create, debug, and maintain. The elegant threading provides a simple route to parallelism on shared-memory machines. Anticipating great improvements in numerical performance, this paper presents a suite of simple programs that indicate how a pure Java Navier-Stokes solver might perform. The suite includes a parallel Euler solver. We present results from a 32-processor Hewlett-Packard machine and a 4-processor Sun server. While speedup is excellent on both machines, indicating a high-quality thread scheduler, the single-processor performance needs much improvement

Requirements for multidisciplinary design of aerospace vehicles on high performance computers

The design of aerospace vehicles is becoming increasingly complex as the various contributing disciplines and physical components become more tightly coupled. This coupling leads to computational problems that will be tractable only if significant advances in high performance computing systems are made. Some of the modeling, algorithmic and software requirements generated by the design problem are discussed

Parallelization of implicit finite difference schemes in computational fluid dynamics

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed