Gary A. Dilts

MOVING-LEAST-SQUARES-PARTICLE HYDRODYNAMICS-I. CONSISTENCY AND STABILITY

The Smooth-Particle-Hydrodynamics (SPH) method is derived in a novel manner by means of a Galerkin approximation applied to the Lagrangian equations of continuum mechanics as in the finite-element method. This derivation is modified to replace the SPH interpolant with the Moving-Least-Squares (MLS) interpolant of Lancaster and Saulkaskas, and define a new particle volume which ensures thermodynamic compatibility. A variable-rank modification of the MLS interpolants which retains their desirable summation properties is introduced to remove the singularities that occur when divergent flow reduces the number of neighbours of a particle to less than the minimum required. A surprise benefit of the Galerkin SPH derivation is a theoretical justification of a common ad hoc technique for variable-h SPH. The new MLSPH method is conservative if an anti-symmetric quadrature rule for the stiffness matrix elements can be supplied. In this paper, a simple one-point collocation rule is used to retain similarity with SPH, leading to a non-conservative method. Several examples document how MLSPH renders dramatic improvements due to the linear consistency of its gradients on three canonical difficulties of the SPH method: spurious boundary effects, erroneous rates of strain and rotation and tension instability. Two of these examples are non-linear Lagrangian patch tests with analytic solutions with which MLSPH agrees almost exactly. The examples also show that MLSPH is not absolutely stable if the problems are run to very long times. A linear stability analysis explains both why it is more stable than SPH and not yet absolutely stable and an argument is made that for realistic dynamic problems MLSPH is stable enough. The notion of coherent particles, for which the numerical stability is identical to the physical stability, is introduced. The new method is easily retrofitted into a generic SPH code and some observations on performance are made. Copyright

Three-dimensional boundary detection for particle methods

The three-dimensional exposure method for the detection of the boundary of a set of overlapping spheres is presented. Like the two-dimensional version described in a previous paper, the three-dimensional algorithm precisely detects void opening or closure, and is optimally suited to the kernel-mediated interactions of smoothed-particle hydrodynamics, although it may be used in any application involving sets of overlapping spheres. The principle idea is to apply the two-dimensional method, on the surface of each candidate boundary sphere, to the circles of intersection with neighboring spheres. As the algorithm finds the exact solution, the quality of detection is independent of particle configuration, in contrast to gradient-based techniques. The observed CPU execution times scale as O(MN?), where M is the number of particles, N is the average number of neighbors of a particle, and ? is a problem-dependent constant between 1.6 and 1.7. The time required per particle is comparable to the amount of time required to evaluate a three-dimensional linear moving-least-squares interpolant at a single point.

A parallel multi-domain solution methodology applied to nonlinear thermal transport problems in nuclear fuel pins

This paper describes an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors is described. Details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstrating the achieved efficiency of the algorithm are presented. Furthermore, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.

Consistent thermodynamic derivative estimates for tabular equations of state.

A valid fluid equation of state (EOS) must satisfy the thermodynamic conditions of consistency (derivation from a free energy) and stability (positive sound speed squared). Numerical simulations of compressible fluid flow for realistic materials require a tabular EOS, but typical software interfaces to such tables based on polynomial or rational interpolants may enforce the stability conditions, but do not enforce the consistency condition and its derivatives. The consistency condition is important for the computation of various dimensionless parameters of an EOS that may involve derivatives of up to second order which are important for the development of more sensitive artificial viscosities and Riemann solvers that accurately model shock structure in regions near phase transitions. We describe a table interface based on the tuned regression method, which is derived from a constrained local least-squares regression technique. It is applied to several SESAME EOS showing how the consistency and stability conditions can be satisfied to round-off while computing first and second derivatives with demonstrated second-order convergence. An improvement of 14 orders of magnitude over conventional derivatives is demonstrated, although the method is apparently two orders of magnitude slower, due to the fact that every evaluation requires solving an 11-dimensional nonlinear system. Application is made to the computation of the fundamental derivative.

Chaotic plane-wave solutions for the relativistic self-interacting quantum electron

Abstract An indication of the chaotic nature of the plane-wave solutions of the coupled Maxwell-Dirac equations is made via numerical integration. The system has a Hamiltonian H, and for H 0 the solutions are chaotic, with an information dimension of ∼ 3.8. The electric and magnetic fields, and the current densities are either identically zero, or average numerically to near zero, providing a consistent, self-contained classical model of vacuum fluctuations.

Fiscal Year 2011 Infrastructure Refactorizations in AMP

In Fiscal Year 2011 (FY11), the AMP (Advanced MultiPhysics) Nuclear Fuel Performance code [1] went through a thorough review and refactorization based on the lessons-learned from the previous year, in which the version 0.9 of the software was released as a prototype. This report describes the refactorization work that has occurred or is in progress during FY11.