A New Discrete Implicit Monte Carlo Scheme for Simulating Radiative Transfer Problems

We present a new algorithm for radiative transfer—based on a statistical Monte Carlo approach—that does not suffer from teleportation effects, on the one hand, and yields smooth results, on the other hand. Implicit Monte Carlo (IMC) techniques for modeling radiative transfer have existed from the 1970s. When they are used for optically thick problems, however, the basic algorithm suffers from “teleportation” errors, where the photons propagate faster than the exact physical behavior, due to the absorption-blackbody emission processes. One possible solution is to use semianalog Monte Carlo, in its new implicit form (ISMC), which uses two kinds of particles, photons and discrete material particles. This algorithm yields excellent teleportation-free results, but it also produces noisier solutions (relative to classic IMC), due to its discrete nature. Here, we derive a new Monte Carlo algorithm, Discrete Implicit Monte Carlo (DIMC), which also uses the idea of two kinds of discrete particles, and thus does not suffer from teleportation errors. DIMC implements the IMC discretization and creates new radiation photons for each time step, unlike ISMC. Using the continuous absorption technique, DIMC yields smooth results like classic IMC. One of the main elements of the algorithm is the avoidance of the explosion of the particle population, by using particle merging. We test the new algorithm on 1D and 2D cylindrical problems, and show that it yields smooth, teleportation-free results. We finish by demonstrating the power of the new algorithm on a classic radiative hydrodynamic problem—an opaque radiative shock wave. This demonstrates the power of the new algorithm for astrophysical scenarios.

Methodology for Determining the Thermal and Thermal-Stress States of a Concrete Storage Container for Spent Nuclear Fuel for Assessment of Its Service Life

The work is devoted to the development of methodologies for determining the thermal and thermal-stress states of the main equipment in dry container storage facilities for spent nuclear fuel. Storage facilities of this type are most common for spent fuel of nuclear power reactors. The safety of storage equipment in terms of assessing its service life is not covered widely enough in the world scientific literature. In particular, there are no effective methods for calculating the thermal and thermal-stress states of the equipment that would take into account the influence of many external factors throughout the life of a storage facility. To assess the thermal state of the containers, forward conjugate heat transfer problems, accounting for the mutual heat transfer in both a solid body and in the fluid environment (air), are proposed to be solved. Based on the solution of the conjugate heat transfer problems, the boundary conditions are to be determined to further assess the thermal-stress state of storage containers using inverse heat transfer problems. The proposed approach to determining the thermal and thermal-stress states of a concrete spent fuel container will promote more effective methods for assessing the service life of dry spent fuel storage facilities, which is, in turn, necessary in the development of ageing management programs for storage equipment and long-term safe operation.

Efficient Simulations of Large Scale Convective Heat Transfer Problems

We describe an approach for efficient solution of large scale convective heat transfer problems, formulated as coupled unsteady heat conduction and incompressible fluid flow equations. The original problem is discretized in time using classical implicit methods, while stabilized finite elements are used for space discretization. The algorithm employed for the discretization of the fluid flow problem uses Picard's iterations to solve the arising nonlinear equations. Both problems, heat transfer and Navier-Stokes quations, give rise to large sparse systems of linear equations. The systems are solved using iterative GMRES solver with suitable preconditioning. For the incompressible flow equations we employ a special preconditioner based on algebraic multigrid (AMG) technique. The paper presents algorithmic and implementation details of the solution procedure, which is suitably tuned, especially for ill conditioned systems arising from discretizations of incompressible Navier-Stokes equations. We describe parallel implementation of the solver using MPI and elements of PETSC library. The scalability of the solver is favourably compared with other methods such as direct solvers and standard GMRES method with ILU preconditioning.

Solving bio-heat transfer multi-layer equation using Green’s Functions method

An analytical method using Green’s Functions for obtaining solutions in bio-heat transfer problems, modeled by Pennes’ Equation, is presented. Mathematical background on how treating Pennes’ equation and its μ2T term is shown, and two contributions to the classical numbering system in heat conduction are proposed: inclusion of terms to specify the presence of the fin term, μ2T, and identify the biological heat transfer problem. The presentation of the solution is made for a general multi-layer domain, deriving and showing general approaches and Green’s Functions for such n number of layers. Numerical examples are presented to simplify human skin as a two-layer domain: dermis and epidermis, accounting metabolism as a heat source, and blood perfusion only at the dermis. Time-independent summations in the series-solution are written in closed forms, leading to better convergence along the boundaries. Details on obtaining the two-layer solution and its eigenvalues are presented for boundary conditions of prescribed temperature inside the body and convection at the surface, such as its intrinsic verification.