Coupling of adaptive refinement with variational multiscale element free Galerkin method for high gradient problems

In this thesis, a new adaptive refinement coupled with variational multiscale element free Galerkin method (EFGM) is developed for solving high gradient problems. The aim of this thesis is to propose a new framework of moving least squares (MLS) approximation with coupling method based on the variational multiscale concept. Additional new nodes will be inserted automatically at high gradient regions by adaptive algorithm based on refinement criteria. An enrichment function is embedded in the MLS approximation for the fine scale part of the problem. Besides, this new technique will be parallelized by using OpenMP which is based on shared memory architecture. The proposed new approach is first applied in two-dimensional large localized gradient problem, transient heat conduction problem as well as Burgers' equation in order to analyze the accuracy of the proposed method and validated with an available analytic solutions. The obtained numerical results show a very good agreement with the analytic solutions and is able to obtain more accurate results than the standard EFGM. It is found that the average relative error of this new method is reduced in the range of 15% to 70%. Besides, this new method is also extended to solve two-dimensional sine-Gordon solitons. The results obtained show good agreement with the published results. Moreover, the parallelization of adaptive variational multiscale EFGM can improve the computational efficiency by reducing the execution time without loss of accuracy. Therefore, the capability and robustness of this new method has the potential to investigate more complicated problems in order to produce higher precision solutions with shorter computational time

Doctor of Philosophy

dissertationRecent trends in high performance computing present larger and more diverse computers using multicore nodes possibly with accelerators and/or coprocessors and reduced memory. These changes pose formidable challenges for applications code to attain scalability. Software frameworks that execute machine-independent applications code using a runtime system that shields users from architectural complexities oer a portable solution for easy programming. The Uintah framework, for example, solves a broad class of large-scale problems on structured adaptive grids using fluid-flow solvers coupled with particle-based solids methods. However, the original Uintah code had limited scalability as tasks were run in a predefined order based solely on static analysis of the task graph and used only message passing interface (MPI) for parallelism. By using a new hybrid multithread and MPI runtime system, this research has made it possible for Uintah to scale to 700K central processing unit (CPU) cores when solving challenging fluid-structure interaction problems. Those problems often involve moving objects with adaptive mesh refinement and thus with highly variable and unpredictable work patterns. This research has also demonstrated an ability to run capability jobs on the heterogeneous systems with Nvidia graphics processing unit (GPU) accelerators or Intel Xeon Phi coprocessors. The new runtime system for Uintah executes directed acyclic graphs of computational tasks with a scalable asynchronous and dynamic runtime system for multicore CPUs and/or accelerators/coprocessors on a node. Uintah's clear separation between application and runtime code has led to scalability increases without significant changes to application code. This research concludes that the adaptive directed acyclic graph (DAG)-based approach provides a very powerful abstraction for solving challenging multiscale multiphysics engineering problems. Excellent scalability with regard to the different processors and communications performance are achieved on some of the largest and most powerful computers available today

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge

Parallel computing 2011, ParCo 2011: book of abstracts

This book contains the abstracts of the presentations at the conference Parallel Computing 2011, 30 August - 2 September 2011, Ghent, Belgiu

Progress Toward Affordable High Fidelity Combustion Simulations Using Filtered Density Functions for Hypersonic Flows in Complex Geometries

Significant progress has been made in the development of subgrid scale (SGS) closures based on a filtered density function (FDF) for large eddy simulations (LES) of turbulent reacting flows. The FDF is the counterpart of the probability density function (PDF) method, which has proven effective in Reynolds averaged simulations (RAS). However, while systematic progress is being made advancing the FDF models for relatively simple flows and lab-scale flames, the application of these methods in complex geometries and high speed, wall-bounded flows with shocks remains a challenge. The key difficulties are the significant computational cost associated with solving the FDF transport equation and numerically stiff finite rate chemistry. For LES/FDF methods to make a more significant impact in practical applications a pragmatic approach must be taken that significantly reduces the computational cost while maintaining high modeling fidelity. An example of one such ongoing effort is at the NASA Langley Research Center, where the first generation FDF models, namely the scalar filtered mass density function (SFMDF) are being implemented into VULCAN, a production-quality RAS and LES solver widely used for design of high speed propulsion flowpaths. This effort leverages internal and external collaborations to reduce the overall computational cost of high fidelity simulations in VULCAN by: implementing high order methods that allow reduction in the total number of computational cells without loss in accuracy; implementing first generation of high fidelity scalar PDF/FDF models applicable to high-speed compressible flows; coupling RAS/PDF and LES/FDF into a hybrid framework to efficiently and accurately model the effects of combustion in the vicinity of the walls; developing efficient Lagrangian particle tracking algorithms to support robust solutions of the FDF equations for high speed flows; and utilizing finite rate chemistry parametrization, such as flamelet models, to reduce the number of transported reactive species and remove numerical stiffness. This paper briefly introduces the SFMDF model (highlighting key benefits and challenges), and discusses particle tracking for flows with shocks, the hybrid coupled RAS/PDF and LES/FDF model, flamelet generated manifolds (FGM) model, and the Irregularly Portioned Lagrangian Monte Carlo Finite Difference (IPLMCFD) methodology for scalable simulation of high-speed reacting compressible flows

Efficient algorithms for the realistic simulation of fluids

Nowadays there is great demand for realistic simulations in the computer graphics field. Physically-based animations are commonly used, and one of the more complex problems in this field is fluid simulation, more so if real-time applications are the goal. Videogames, in particular, resort to different techniques that, in order to represent fluids, just simulate the consequence and not the cause, using procedural or parametric methods and often discriminating the physical solution. This need motivates the present thesis, the interactive simulation of free-surface flows, usually liquids, which are the feature of interest in most common applications. Due to the complexity of fluid simulation, in order to achieve real-time framerates, we have resorted to use the high parallelism provided by actual consumer-level GPUs. The simulation algorithm, the Lattice Boltzmann Method, has been chosen accordingly due to its efficiency and the direct mapping to the hardware architecture because of its local operations. We have created two free-surface simulations in the GPU: one fully in 3D and another restricted only to the upper surface of a big bulk of fluid, limiting the simulation domain to 2D. We have extended the latter to track dry regions and is also coupled with obstacles in a geometry-independent fashion. As it is restricted to 2D, the simulation loses some features due to the impossibility of simulating vertical separation of the fluid. To account for this we have coupled the surface simulation to a generic particle system with breaking wave conditions; the simulations are totally independent and only the coupling binds the LBM with the chosen particle system. Furthermore, the visualization of both systems is also done in a realistic way within the interactive framerates; raycasting techniques are used to provide the expected light-related effects as refractions, reflections and caustics. Other techniques that improve the overall detail are also applied as low-level detail ripples and surface foam