Related papers: An Accurate S$_N$ Method for Solving Static Multig…
The nonclassical transport equation models particle transport processes in which the particle flux does not decrease as an exponential function of the particle's free-path. Recently, a spectral approach was developed to generate…
We present a genetic programming approach to automatically discover convergence acceleration methods for discrete ordinates solutions of neutron transport problems in slab geometry. Classical acceleration methods such as Aitken's…
We present a numerical method for handling the resolution of a general transport equation for radiative particles, aimed at physical problems with a general spherical geometry. Having in mind the computational time difficulties encountered…
A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our…
This work introduces a scaffolding framework to compactly parametrise solid structures with conforming NURBS elements for isogeometric analysis. A novel formulation introduces a topological, geometrical and parametric subdivision of the…
In this work, we present a subdomain discontinuous least-squares (SDLS) scheme for neutronics problems. Least-squares (LS) methods are known to be inaccurate for problems with sharp total-cross section interfaces. In addition, the…
In this work, we extend the solid harmonics derivation, which was used by Ackroyd et al to derive the steady-state SP$_N$ equations, to transient problems. The derivation expands the angular flux in ordinary surface harmonics but uses…
The high-order accurate continuous Galerkin finite element method offers attractive computational efficiency for computational fluid dynamics. A challenge is however spurious oscillations which result for convection dominated flows over…
Transport phenomena-describing the movement of particles, energy, or other physical quantities-are fundamental in various scientific disciplines, including nuclear physics, plasma physics, astrophysics, engineering, and the natural…
We extend the analytical multigroup $S_N$ method to solve 1D fixed source problems. The fixed source solver is applied in power iteration of eigenvalue problems.
An improvement modification of the Spectral Approach (SA) used for approximating the nonclassical neutral particle transport equation is described in this work. The main focus of the modified SA lies on a slight modification of the…
A method for the fast and accurate solution of the radiative transfer equation in plane-parallel media with coherent isotropic scattering is presented. This largely analytical approach uses the formalism of meromorphic functions in order to…
We present a numerical method for solving the time-independent thermal radiative transfer (TRT) equation or the neutron transport (NT) equation when the opacity or cross-section varies rapidly in energy (frequency). The approach is based on…
The use of machine learning algorithms to address classification problems is on the rise in many research areas. The current study is aimed at testing the potential of using such algorithms to auto-select the best solvers for transport…
In this work we present two new closures for the spherical harmonics (PN) method in slab geometry transport problems. Our approach begins with an analysis of the squared-residual of the transport equation where we show that the standard…
An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…
A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and…
We have coded a Boltzmann solver based on a finite difference scheme (S_N method) aiming at calculations of neutrino transport in type II supernovae. Close comparison between the Boltzmann solver and a Monte Carlo transport code has been…
This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle…
This paper is concerned with the approximation of the radiative transfer equation for a grey medium in the slab geometry by the moment method. We develop a novel moment model inspired by the classical $P_N$ model and $M_N$ model. The new…