Paul Orkwis

Department Head and Professor of Aerospace Engineering and Engineering Mechanics
Department of Aerospace Engineering and Engineering Mechanics
University of Cincinnati

"Development of an Implicit, Overset High-Order Discontinuous Galerkin Simulation Framework"

Guggenheim 442 @ 3:30pm

Abstract:
The discontinuous Galerkin(DG) method for discretizing partial differential equations has been applied in many fields including acoustics, numerical weather predictions, and aerodynamics. Part of the strength of the method exists in its ability to provide arbitrary high-order accuracy, while maintaining a local computational stencil. The local scheme is attractive for use on unstructured grids but is also advantageous for Chimera/Overset structured grids, where traditional challenges with overset schemes such as orphan nodes are eliminated. The ability to represent curved geometry also reduces discretization and interpolation error. The combination of high-order accuracy and straight-forward geometry representation and modification makes the Chimera/Overset-DG discretization an attractive core capability for a framework enabling analysis, modeling, and design.

Researchers at the University of Cincinnati Gas Turbine Simulation Laboratory have been driving sustained development of Chimera/Overset-DG capabilities for several years. More recently, they have combined lessons learned from previous development efforts and created a software framework based on a core Chimera/Overset-DG capability and thoughtful software engineering. The project is ChiDG: a Chimera-based discontinuous Galerkin framework. The framework is equipped with abstractions for many common components in numerical methods such as time-integrators, nonlinear/linear solvers, and preconditioners so new developers do not have to reinvent the infrastructure and interactions between these components. Additionally, the framework takes a composition-based approach to representing equations. Abstractions exist for defining model coefficients, numerical operators, and composing equation sets from these components. From a software perspective, the framework is written in Modern Fortran(F90-2008), uses CMake and pFUnit to automate configure/build/test activities, and includes an intrinsic automatic differentiation capability to reduce developer burden when implementing new models. The project is open-source under the BSD 3-clause license and hosted on GitHub along with documentation(https://github.com/nwukie/ChiDG).

The framework currently includes Newton-based nonlinear solvers with some globalization approaches for robustness, an FGMRES linear solver, a parallel ILU0 preconditioner, and Euler/RANS equation sets with a Spalart-Allmaras turbulence model. Recent efforts on the ChiDG framework have included the addition of high-order implicit time-integrators along with a Harmonic Balance time-integrator for time-spectral problems. An Arbitrary Lagrangian Eulerian formulation was also added enabling problems with mesh motion or rotating/translating coordinate systems. Current efforts on the ChiDG framework are focused on enabling capabilities for applied problems in external aerodynamics and turbomachinery as well as incorporating adjoint capabilities to drive design and optimization efforts. This talk will discuss the development of ChiDG and provide examples of its capability.