Russell Hooper

Final Report on LDRD Project: Coupling Strategies for Multi-Physics Applications

Many current and future modeling applications at Sandia including ASC milestones will critically depend on the simultaneous solution of vastly different physical phenomena. Issues due to code coupling are often not addressed, understood, or even recognized. The objectives of the LDRD has been both in theory and in code development. We will show that we have provided a fundamental analysis of coupling, i.e., when strong coupling vs. a successive substitution strategy is needed. We have enabled the implementation of tighter coupling strategies through additions to the NOX and Sierra code suites to make coupling strategies available now. We have leveraged existing functionality to do this. Specifically, we have built into NOX the capability to handle fully coupled simulations from multiple codes, and we have also built into NOX the capability to handle Jacobi Free Newton Krylov simulations that link multiple applications. We show how this capability may be accessed from within the Sierra Framework as well as from outside of Sierra. The critical impact from this LDRD is that we have shown how and have delivered strategies for enabling strong Newton-based coupling while respecting the modularity of existing codes. This will facilitate the use of these codes in a coupled manner to solve multi-physic applications.

A theory manual for multi-physics code coupling in LIME.

The Lightweight Integrating Multi-physics Environment (LIME) is a software package for creating multi-physics simulation codes. Its primary application space is when computer codes are currently available to solve different parts of a multi-physics problem and now need to be coupled with other such codes. In this report we define a common domain language for discussing multi-physics coupling and describe the basic theory associated with multiphysics coupling algorithms that are to be supported in LIME. We provide an assessment of coupling techniques for both steady-state and time dependent coupled systems. Example couplings are also demonstrated.

Intelligent Nonlinear Solvers for Computational Fluid Dynamics

Implicit nonlinear solvers for solving systems of nonlinear PDEs are very powerful. Many compressible flow codes utilize Newton-Krylov (NK) methods and matrix-free NewtonKrylov (MFNK) methods for a range of flow regimes and different flow models such as inviscid, laminar, turbulent and reacting flows. One drawback is that these solvers are complex requiring the specification of many settings. Expertise is necessary to achieve high performance. There is a need to develop ”intelligent nonlinear solvers” that are capable of changing settings dynamically and adapting to evolving solutions and changing solver performance, in order to reduce the burden on the user, and improve overall efficiency and reliability. In this paper we take the first steps in achieving automatic control of nonlinear solvers for compressible flows by combining semi- and fully- implicit solver strategies in ways that utilizes them more efficiently than simply applying one method or another during the entire solution procedure. The understanding gained from this work will lay the groundwork for future development of more autonomous ”intelligent solvers”. Implicit solvers are widely used to in compuational fluid dynamic applications to obtain steady-state solutions to the equations governing fluid flow. Semi-implicit (point-implicit) methods are one of the most common. Semi-implicit methods are relatively easy to implement, have low memory requirements and can march at large time step sizes compared to explicit methods. Semi-implicit iterations are only modestly more expensive than explicit iterations and tend to converge linearly. They are also robust in the sense that they are relatively easy to use. However, convergence ”stalling” can be a problem in certain circumstances. In recent years, Newton-Krylov (NK) methods are becoming more popular. NK methods are less straight forward to use and more expensive per iteration than semi-implicit methods. However, NK methods are very efficient for as the solution is approached in an iterative sense, quadratic convergence rates can be achieved. Very large time steps can be used to advance the solution to steady-state. They are also robust due to the effectiveness of Krylov subspace iterative linear solvers. In both methods, solutions are achieved iteratively by solving a series of nonlinear problems where the system equations are linearized and then solved with an iterative linear solver. Semi-implicit solvers combine the nonlinear and linear loops together, solving a modified linear system less accurately but more cheaply. Typically, semi-implicit solvers are cheaper than NK methods in the beginning when the CFL is small and the linear systems are dominated by a large diagonal inertia term. Later, as the inertia term becomes smaller, the linear problem becomes more difficult to solve and NK methods become more efficient. Therefore, it would make sense to combine these approaches in a single solver stategy.

Enabling Fluid-Structural Strong Thermal Coupling Within a Multi-Physics Environment

We demonstrate use of a Jacobian-Free Newton-Krylov solver to enable strong thermal coupling at the interface between a solid body and an external compressible fluid. Our method requires only information typically used in loose coupling based on successive substitution and is implemented within a multi-physics framework. We present results for two external flows over thermally conducting solid bodies obtained using both loose and strong coupling strategies. Performance of the two strategies is compared to elucidate both advantages and caveats associated with strong coupling.

Aleph Field Solver Challenge Problem Results Summary

Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched mod- eling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Alephs complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Alephs field solver via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challeng- ing problems important to Sandias mission that Aleph was specifically designed to address.

Boltzmann-Electron Model in Aleph.

We apply the Boltzmann-electron model in the electrostatic, particle-in-cell, finite- element code Aleph to a plasma sheath. By assuming a Boltzmann energy distribution for the electrons, the model eliminates the need to resolve the electron plasma fre- quency, and avoids the numerical %22grid instability%22 that can cause unphysical heating of electrons. This allows much larger timesteps to be used than with kinetic electrons. Ions are treated with the standard PIC algorithm. The Boltzmann-electron model re- quires solution of a nonlinear Poisson equation, for which we use an iterative Newton solver (NOX) from the Trilinos Project. Results for the spatial variation of density and voltage in the plasma sheath agree well with an analytic model

3D vacuum ARC breakdown simulation: Many challenges and some solutions

Summary form only given. We present our current capabilities and plans targeting the simulation of 3D vacuum arc discharge in realistic geometries. Vacuum arc discharge is an incredibly challenging problem due to the enormous dynamic changes in plasma growth, collisional processes, and time scales. Our simulation model targets a co-planar Cu-Cu vacuum breakdown experiment. We will estimate the computational requirements for this physically relevant breakdown system assuming a fully kinetic description. A fully kinetic description is required to accurately capture the initial breakdown. Progress on unstructured mesh collisional PIC methodology, dynamic particle weighting, managing multiple temporal and spatial scales, electrode models, and efficient parallel scaling will be addressed.