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

Abstract

Abstract. 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.

Overview of the incompressible Navier–Stokes simulation capabilities in the MOOSE framework

“…The MOOSE framework is a general purpose toolkit in the vein of other popular, customizable C ++ FEM libraries such as deal.II [64], DUNE [65], GRINS [66], FreeFem ++ [67], Open-FOAM [68], and the computational back end of FEniCS, DOLFIN [69]. Generally speaking, these libraries are designed to enable practitioners who are familiar with the engineering and applied mathematics aspects of their application areas (that is, who already have a mathematical model and associated variational statement) to translate those methods from "pen and paper" descriptions into portable, extensible, well supported, high performance software.…”

Enabling the Statistical Calibration of Active Nitridation of Graphite by Atomic Nitrogen

“…10, 11, 12 Given the flow conditions in the experiment, the mesh resolution needed to adequately resolve the quantities of interest also adequately resolve the convection scales of the problem and, therefore, no numerical stabilization is used. We use the Taylor-Hood velocity/pressure elements as well as second order approximations in temperature and species.…”

“…For each independent geometry, an independent mesh is created. d The mesh is constructed using adaptive mesh refinement (AMR) using adjoint-based error estimates 14,15 in the both the quantities of interest (QoIs) (12) and (14). From the final adapted mesh for each scenario, the mesh was uniformly refined up to three times in order to assess the convergence of the QoIs.…”

“…Furthermore, the evaluation of the interpolation points can be done independently, facilitating parallel construction of the surrogate. We use infrastructure in the QUESO 18 library, in conjunction with GRINS, 12 to construct these surrogate models. Figure 5 illustrates the output for the two QoIs for dataset A-1-13a.…”

Approaches for mitigating over‐solving in multiphysics simulations

“…Recently, many codes have been developed to address the challenges of multiphysics simulation and enable high‐fidelity predictive capabilities. Examples of computational frameworks built for solving multiphysics problems are numerous .…”