Stochastic collocation on unstructured multivariate meshes

Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction are becoming standard tools used in a variety of applications. Selection of a collocation mesh is frequently a challenge, but methods that construct geometrically "unstructured" collocation meshes have shown great potential due to attractive theoretical properties and direct, simple generation and implementation. We investigate properties of these meshes, presenting stability and accuracy results that can be used as guides for generating stochastic collocation grids in multiple dimensions.Comment: 29 pages, 6 figure

Doctor of Philosophy

dissertationRadiation is the dominant mode of heat transfer in high temperature combustion environments. Radiative heat transfer affects the gas and particle phases, including all the associated combustion chemistry. The radiative properties are in turn affected by the turbulent flow field. This bi-directional coupling of radiation turbulence interactions poses a major challenge in creating parallel-capable, high-fidelity combustion simulations. In this work, a new model was developed in which reciprocal monte carlo radiation was coupled with a turbulent, large-eddy simulation combustion model. A technique wherein domain patches are stitched together was implemented to allow for scalable parallelism. The combustion model runs in parallel on a decomposed domain. The radiation model runs in parallel on a recomposed domain. The recomposed domain is stored on each processor after information sharing of the decomposed domain is handled via the message passing interface. Verification and validation testing of the new radiation model were favorable. Strong scaling analyses were performed on the Ember cluster and the Titan cluster for the CPU-radiation model and GPU-radiation model, respectively. The model demonstrated strong scaling to over 1,700 and 16,000 processing cores on Ember and Titan, respectively

Mesh generation for voxel -based objects

A new physically-based approach to unstructured mesh generation via Monte-Carlo simulation is proposed. Geometrical objects to be meshed are represented by systems of interacting particles with a given interaction potential. A new way of distributing nodes in complex domains is proposed based on a concept of dynamic equilibrium ensemble, which represents a liquid state of matter. The algorithm is simple, numerically stable and produces uniform node distributions in domains of complex geometries and different dimensions. Well-shaped triangles or tetrahedra can be created by connecting a set of uniformly-spaced nodes. The proposed method has many advantages and potential applications.;The new method is applied to the problem of meshing of voxel-based objects. By customizing system potential energy function to reflect surface features, particles can be distributed into desired locations, such as sharp corners and edges. Feature-preserved surface mesh can then be constructed by connecting the node set.;A heuristic algorithm using an advancing front approach is proposed to generate triangulated surface meshes on voxel-based objects. The resultant surface meshes do not inherit the anisotropy of the underlying hexagonal grid. However, the important surface features, such as edges and corners may not be preserved in the mesh.;To overcome this problem, surface features such as edges, corners need to be detected. A new approach of edge capturing is proposed and demonstrated. The approach is based on a Laplace solver with incomplete Jacobi iterations, and as such is very simple and efficient. This edge capturing approach combined with the mesh generation methods above forms a simple and robust technique of unstructured mesh generation on voxel-based objects.;A graphical user interface (GUI) capable of complex geometric design and remote simulation control was implemented. The GUI was used in simulations of large fuel-cell stacks. It enables one to setup, run and monitor simulations remotely through secure shell (SSH2) connections. A voxel-based 3D geometrical modeling module is built along with the GUI. The flexibility of voxel-based geometry representation enables one to use this technique for both geometric design and visualization of volume data

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

An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries

This paper presents the results of validation of an open source Direct Simulation Monte Carlo (DSMC) code for general application to rarefied gas flows. The new DSMC code, called dsmcFoam, has been written within the framework of the open source C++ CFD toolbox OpenFOAM. The main features of dsmcFoam code include the capability to perform both steady and transient solutions, to model arbitrary 2D/3D geometries, and unlimited parallel processing. Test cases have been selected to cover a wide range of benchmark examples from 1D to 3D. These include relaxation to equilibrium, 2D flow over a flat plate and a cylinder, and 3D supersonic flows over complex geometries. In all cases, dsmcFoam shows very good agreement with data provided by both analytical solutions and other contemporary DSMC codes

Efficient parallel solver for high-speed rarefied gas flow using GSIS

Recently, the general synthetic iterative scheme (GSIS) has been proposed to find the steady-state solution of the Boltzmann equation in the whole range of gas rarefaction, where its fast-converging and asymptotic-preserving properties lead to the significant reduction of iteration numbers and spatial cells in the near-continuum flow regime. However, the efficiency and accuracy of GSIS has only been demonstrated in two-dimensional problems with small numbers of spatial cell and discrete velocities. Here, a large-scale parallel computing strategy is designed to extend the GSIS to three-dimensional high-speed flow problems. Since the GSIS involves the calculation of the mesoscopic kinetic equation which is defined in six-dimensional phase-space, and the macroscopic high-temperature Navier-Stokes-Fourier equations in three-dimensional physical space, the proper partition of the spatial and velocity spaces, and the allocation of CPU cores to the mesoscopic and macroscopic solvers, are the keys to improving the overall computational efficiency. These factors are systematically tested to achieve optimal performance, up to 100 billion spatial and velocity grids. For hypersonic flows around the Apollo reentry capsule, the X38-like vehicle, and the space station, our parallel solver can get the converged solution within one hour