Paul T. Bauman

MultiScale Modeling of Physical Phenomena: Adaptive Control of Models

It is common knowledge that the accuracy with which computer simulations can depict physical events depends strongly on the choice of the mathematical model of the events. Perhaps less appreciated is the notion that the error due to modeling can be defined, estimated, and used adaptively to control modeling error, provided one accepts the existence of a base model that can serve as a datum with respect to which other models can be compared. In this work, it is shown that the idea of comparing models and controlling model error can be used to develop a general approach for multiscale modeling, a subject of growing importance in computational science. A posteriori estimates of modeling error in so-called quantities of interest are derived and a class of adaptive modeling algorithms is presented. Several applications of the theory and methodology are presented. These include preliminary work on random multiphase composite materials, molecular statics simulations with applications to problems in nanoindentation, and analysis of molecular dynamics models using various techniques for scale bridging.

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.

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.