Kyle K. Chand

A composite grid solver for conjugate heat transfer in fluid-structure systems

We describe a numerical method for modeling temperature-dependent fluid flow coupled to heat transfer in solids. This approach to conjugate heat transfer can be used to compute transient and steady state solutions to a wide range of fluid-solid systems in complex two- and three-dimensional geometry. Fluids are modeled with the temperature-dependent incompressible Navier-Stokes equations using the Boussinesq approximation. Solids with heat transfer are modeled with the heat equation. Appropriate interface equations are applied to couple the solutions across different domains. The computational region is divided into a number of sub-domains corresponding to fluid domains and solid domains. There may be multiple fluid domains and multiple solid domains. Each fluid or solid sub-domain is discretized with an overlapping grid. The entire region is associated with a composite grid which is the union of the overlapping grids for the sub-domains. A different physics solver (fluid solver or solid solver) is associated with each sub-domain. A higher-level multi-domain solver manages the entire solution process.We propose and analyze some centered discrete approximations to the interface equations that have some desirable stability properties. The coupled interface equations may be solved directly when using explicit time-stepping methods in the sub-domains, resulting in a strongly coupled approach. The stability of the interface treatment in this case is independent of the relative sizes of the material properties in the two domains with the time-step only depending on the usual von Neumann conditions for each sub-domain. For implicit time-stepping methods we solve the interface equations in a weakly coupled fashion to avoid forming a coupled implicit system across all sub-domains. The convergence of this approach does depend on the relative sizes of the thermal conductivities and diffusivities. We analyze different iteration strategies for solving these implicit equations including the use of mixed (Robin) approximations at the interface.Numerical results are presented to illustrate the method. The accuracy of the technique is verified using the method of analytic solutions and by computing the solution to some heat exchanger problems where the exact solution is known. The technique is also applied to the modeling of an inertial-confinement-fusion hohlraum target and the flow of coolant past an hexagonal array of heated fuel rods. The multi-domain solver runs in parallel on distributed memory computers and some parallel results are provided.

Toward interoperable mesh, geometry and field components for PDE simulation development

Mesh-based PDE simulation codes are becoming increasingly sophisticated and rely on advanced meshing and discretization tools. Unfortunately, it is still difficult to interchange or interoperate tools developed by different communities to experiment with various technologies or to develop new capabilities. To address these difficulties, we have developed component interfaces designed to support the information flow of mesh-based PDE simulations. We describe this information flow and discuss typical roles and services provided by the geometry, mesh, and field components of the simulation. Based on this delineation for the roles of each component, we give a high-level description of the abstract data model and set of interfaces developed by the Department of Energy’s Interoperable Tools for Advanced Petascale Simulation (ITAPS) center. These common interfaces are critical to our interoperability goal, and we give examples of several services based upon these interfaces including mesh adaptation and mesh improvement.

The TSTT Mesh Interface

PDE-based numerical simulation applications commonly use basic software infrastructure to manage mesh, geometry, and discretization data. The commonality of this infrastructure implies the software is theoretically amenable to re-use. However, the traditional reliance on library-based implementations of these functionalities hampers experimentation with different software instances that provide similar functionality. This is especially true for meshing and geometry libraries where applications often directly access the underlying data structures, which can be quite different from implementation to implementation. Thus, using different libraries interchangeably or interoperably for this functionality has proven difficult at best and has hampered the wide spread use of advanced meshing and geometry tools developed by the research community. To address these issues, the Terascale Simulation Tools and Technologies center is working to develop standard interfaces to enable the creation of interoperable and interchangeable simulation tools. In this paper, we focus on a languageand data-structure-independent interface supporting query and modification of mesh data conforming to a general abstract data model. We describe the model and interface, and provide programming “best practices” recommendations based on early experience implementing and using the interface.