Engineering topics

McClarren, Ryan G.

Publications and source records attributed to McClarren, Ryan G..

4 records

DOE OSTI2024

A hybrid Monte Carlo, discontinuous Galerkin method for linear kinetic transport equations

Here we present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates use bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to “relabel” collided particles as uncollided particles. In conclusion, from a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A collision-based hybrid method for the BGK equation

In this article, we apply the collision-based hybrid method introduced by Hauck and McClarren to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Multigroup Neutron Transport Using a Collision-Based Hybrid Method

A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the isotropic multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and approximates the fission and scattering sources on the coarser grids. The coupling of a collided transport equation, discretized on the coarse grid, with an uncollided transport equation, discretized on the fine grid, yields an algorithm that, in most cases, is more efficient than the traditional multigroup approach. In conclusion, the improvement over existing techniques is demonstrated for time-dependent problems with different materials, geometries, and energy groups.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Transfer Learning of High-Fidelity Opacity Spectra in Autoencoders and Surrogate Models

Simulations of high energy density physics are expensive, largely in part for the need to produce nonlocal thermodynamic equilibrium opacities. High-fidelity spectra may reveal new physics in the simulations not seen with low-fidelity spectra, but the cost of these simulations also scales with the level of fidelity of the opacities being used. Neural networks are capable of reproducing these spectra, but neural networks need data to train them, which limits the level of fidelity of the training data. Here this article demonstrates that it is possible to reproduce high-fidelity spectra with median errors in the realm of 3%–4% using as few as 50 samples of high-fidelity Krypton data by performing transfer learning on a neural network trained on many times more low-fidelity data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗