Engineering topics

Torrilhon, Manuel

Publications and source records attributed to Torrilhon, Manuel.

3 records

DOE OSTI2018

On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation

We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331–407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) , we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2011

Regularized Grad equations for multicomponent plasmas

The moment method of Grad is used to derive macroscopic conservation equations for multicomponent plasmas for small and moderate Knudsen numbers, accounting for the electromagnetic field influence and thermal nonequilibrium. In the low Knudsen number limit, the equations derived are fully consistent with those obtained by means of the Chapman-Enskog method. In particular, we have retieved the Kolesnikov effect coupling electrons and heavy particles in the case of the Boltzmann moment systems. Finally, a regularization procedure is proposed to achieve continuous shock structures at all Mach numbers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗