Roy H. Stogner

libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations

In this paper we describe the libMesh (http://libmesh.sourceforge.net) framework for parallel adaptive finite element applications. libMesh is an open-source software library that has been developed to facilitate serial and parallel simulation of multiscale, multiphysics applications using adaptive mesh refinement and coarsening strategies. The main software development is being carried out in the CFDLab (http://cfdlab.ae.utexas.edu) at the University of Texas, but as with other open-source software projects; contributions are being made elsewhere in the US and abroad. The main goals of this article are: (1) to provide a basic reference source that describes libMesh and the underlying philosophy and software design approach; (2) to give sufficient detail and references on the adaptive mesh refinement and coarsening (AMR/C) scheme for applications analysts and developers; and (3) to describe the parallel implementation and data structures with supporting discussion of domain decomposition, message passing, and details related to dynamic repartitioning for parallel AMR/C. Other aspects related to C++ programming paradigms, reusability for diverse applications, adaptive modeling, physics-independent error indicators, and similar concepts are briefly discussed. Finally, results from some applications using the library are presented and areas of future research are discussed.

MASA: a library for verification using manufactured and analytical solutions

In this paper we introduce the Manufactured Analytical Solution Abstraction (MASA) library for applying the method of manufactured solutions to the verification of software used for solving a large class of problems stemming from numerical methods in mathematical physics including nonlinear equations, systems of algebraic equations, and ordinary and partial differential equations. We discuss the process of scientific software verification, manufactured solution generation using symbolic manipulation with computer algebra systems such as Maple™ or SymPy, and automatic differentiation for forcing function evaluation. We discuss a hierarchic methodology that can be used to alleviate the combinatorial complexity in generating symbolic manufactured solutions for systems of equations based on complex physics. Finally, we detail the essential features and examples of the Application Programming Interface behind MASA, an open source library designed to act as a central repository for manufactured and analytical solutions over a diverse range of problems.

Loose-coupling algorithm for simulating hypersonic flows with radiation and ablation

Aprocedure has been developed to couple a hypersonic reacting flowmodel, a radiative heat transfermodel, and a surface ablation model to study the surface heat transfer and surface ablation rate of atmospheric reentry vehicles. The two-way loose-coupling algorithm is described for each of the models, as is the solution procedure to achieve convergence. Observations on the challenges of the loose-coupling strategy are given. Representative results are presented for two-dimensional benchmark examples and for three-dimensional flow at an angle of attack past a symmetric capsule based on the Crew Exploration Vehicle reentry vehicle. Effects due to the interaction with radiation and ablation are shown for two quantities of interest: the predicted peak surface heat flux and the ablation rate on the vehicle heat shield. Uncertain parameters are identified in each of the submodels, and a preliminary parameter sensitivity study is carried out by varying these values to examine their effects on the heat transfer and ablation rates in the coupled problem.

GRINS: A Multiphysics Framework Based on the libMesh Finite Element Library

The progression of scientific computing resources has enabled the numerical approximation of mathematical models describing complex physical phenomena. A significant portion of researcher time is typically dedicated to the development of software to compute the numerical solutions. This work describes a flexible C++ software framework, built on the libMesh finite element library, designed to alleviate developer burden and provide easy access to modern computational algorithms, including quantity-of-interest-driven parallel adaptive mesh refinement on unstructured grids and adjoint-based sensitivities. Other software environments are highlighted and the current work motivated; in particular, the present work is an attempt to balance software infrastructure and user flexibility. The applicable class of problems and design of the software components is discussed in detail. Several examples demonstrate the effectiveness of the design, including applications that incorporate uncertainty. Current and planned developments are discussed.

Hierarchical Latin Hypercube Sampling

ABSTRACT Latin hypercube sampling (LHS) is a robust, scalable Monte Carlo method that is used in many areas of science and engineering. We present a new algorithm for generating hierarchic Latin hypercube sets (HLHS) that are recursively divisible into LHS subsets. Based on this new construction, we introduce a hierarchical incremental LHS (HILHS) method that allows the user to employ LHS in a flexibly incremental setting. This overcomes a drawback of many LHS schemes that require the entire sample set to be selected a priori, or only allow very large increments. We derive the sampling properties for HLHS designs and HILHS estimators. We also present numerical studies that showcase the flexible incrementation offered by HILHS.

Multiphysics Coupling for Reentry Flows

A procedure has been developed to couple a hypersonic reacting flow model, a radiative heat transfer model, and a surface ablation model to study the surface heat transfer and surface ablation rate of atmospheric entry vehicles. The “loose” coupling algorithm is described for each of the models as well as the solution procedures to achieve convergence. Observations on the challenges of the loose coupling strategy are given. Representative results are presented for 2-D benchmark examples and for flow at angle of attack past an axisymmetric capsule based on the CEV reentry vehicle. Effects due to the interaction with radiation and ablation are shown for two quantities of interest, the predicted peak surface heat flux and the ablation rate on the vehicle heatshield. Uncertain parameters are identified in each of the submodels, and a parameter sensitivity study is carried out by varying these values to examine their effects on the heat transfer and ablation rates in the coupled prediction.