Neural Network Based Deep Learning Method for Multi-Dimensional Neutron Diffusion Problems with Novel Treatment to Boundary

In this paper, the artificial neural networks (ANN) based deep learning (DL) techniques were developed to solve the neutron diffusion problems for the continuous neutron flux distribution without domain discretization in advance. Due to its mesh-free property, the DL solution can easily be extended to complicated geometries. Two specific realizations of DL methods with different boundary treatments are developed and compared for accuracy and efficiency, including the boundary independent method (BIM) and boundary dependent method (BDM). The performance comparison on analytic benchmark indicates BDM being the preferred DL method. Novel constructions of trial function are proposed to generalize the application of BDM. For a more in-depth understanding of the BDM on diffusion problems, the influence of important hyper-parameters is further investigated. Numerical results indicate that the accuracy of BDM can reach hundreds of times higher than that of BIM on diffusion problems. This work can provide a new perspective for applying the DL method to nuclear reactor calculations.

Development of Smoothed Particle Hydrodynamics for Simulation of Flow and Contaminant Transport on Natural Urban Terrain and Streams

Smoothed Particle Hydrodynamics (SPH) method is proposed, as an alternative mesh-free approach to model all components of rainfall, surface runoff, fluid flow and contaminant transport with the representation of contaminant and fluid, as particles. By doing so, contaminant particles can be traced for the motion within runoff or fluid flow, even in the form of minute concentration which is difficult to render in conventional Eulerian grid methods. Weakly compressible SPH (WCSPH) is selected with cubic spline kernel, and the incorporation of Large Eddy Simulation (LES) representing turbulence effect. Various SPH diffusion formulations have been reviewed and selected. The selected SPH formulation for contaminant concentration is validated against analytical diffusion equation with boundary conditions of solid wall or free surface. The validated method is applied to calculate the overland flow and the contaminant transport on a model terrain and a real terrain geometry. The real terrain is a part of the city of Teluk Intan in Perak, Malaysia and is simulated using digital elevation model (DEM) data retrieved from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Water Body Dataset (ASTWBD) for ground elevation and channel surface.

A comparative study of Desarda’s mesh free inguinal hernia repair with modified Bassini’s repair

Objective. This is a prospective study of 50 cases of inguinal hernias which were treated through open inguinal hernia repair techniques. The study was conducted with the objective of comparing the effectiveness of these procedures and complications. Materials and Methods. A number of 50 cases of inguinal hernias admitted to Dr. BR Ambedkar Medical College and Hospital were selected on the basis of the non-probability (purposive) sampling method. All the patients with direct and indirect uncomplicated hernias treated by means of an open approach were included. After the preoperative preparation, they were randomly chosen either for Desarda’s or Modified Bassini’s repair techniques. Results. In the postoperative period, moderate pain was experienced by 19 patients included in the Desarda group and 17 patients included in the Modified Bassini’s repair group on day 1. The postoperative wound infection developed in 2 cases of Desarda and 3 cases of Modified Bassini’s, erythema was observed in 2 cases of Desarda and 3 cases of Modified Bassini’s, 3 cases reported the occurrence of seroma in the Desarda group and 4 cases of seroma were recorded in the Modified Bassini’s group. Conclusions. The patients who underwent Desarda repair complained of a higher intensity of pain, which could probably be attributed to the extensive dissection involved. The duration of Desarda repair was longer due to the learning curve of the surgeons in our hospital. The return to normal gait and normal activities was significantly lower in the Desarda group. The duration of hospital stays and the postoperative complications was not significantly different in the two groups. There were no recurrences in either of the groups until the current study.

Random walk on spheres algorithm for solving steady-state and transient diffusion-recombination problems

We further develop in this study the Random Walk on Spheres (RWS) stochastic algorithm for solving systems of coupled diffusion-recombination equations first suggested in our recent article [K. Sabelfeld, First passage Monte Carlo algorithms for solving coupled systems of diffusion–reaction equations, Appl. Math. Lett. 88 2019, 141–148]. The random walk on spheres process mimics the isotropic diffusion of two types of particles which may recombine to each other. Our motivation comes from the transport problems of free and bound exciton recombination. The algorithm is based on tracking the trajectories of the diffusing particles exactly in accordance with the probabilistic distributions derived from the explicit representation of the relevant Green functions for balls and spheres. Therefore, the method is mesh free both in space and time. In this paper we implement the RWS algorithm for solving the diffusion-recombination problems both in a steady-state and transient settings. Simulations are compared against the exact solutions. We show also how the RWS algorithm can be applied to calculate exciton flux to the boundary which provides the electron beam-induced current, the concentration of the survived excitons, and the cathodoluminescence intensity which are all integral characteristics of the solution to diffusion-recombination problem.

Optimal location of pumping wells by a mesh-free numerical method

In the present study, the optimal place to excavate extraction wells as the drawdown gets minimized was investigated in a real aquifer. Meshless local Petrov-Galerkin (MLPG) method is used as the simulation method. The closeness of its results to the observational data compared to the finite difference solution showed the higher accuracy of this method as the RMSE for MLPG is 0.757 m while this value for finite difference equaled to 1.197 m. Particle warm algorithm is used as the optimization model. The objective function defined as the summation of the absolute values of difference between the groundwater level before abstraction and the groundwater level after abstraction from wells. In Birjand aquifer which is investigated in transient state, the value of objective function before applying the optimization model was 2.808 m, while in the optimal condition, reached to 1.329 m (47% reduction in drawdown). This fact was investigated and observed in three piezometers. In the first piezometer, the drawdown before and after model enforcement was 0.007 m and 0.003 m, respectively. This reduction occurred in other piezometers as well.

Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials

This paper introduces a novel meshless and Lagrangian approach for simulating non-Newtonian flows, named Lagrangian Differencing Dynamics (LDD). Second-order-consistent spatial operators are used to directly discretize and solve generalized Navier–Stokes equations in a strong formulation. The solution is obtained using a split-step scheme, i.e., by decoupling the solutions of the pressure and velocity. The pressure is obtained by solving a Poisson equation, and the velocity is solved in a semi-implicit formulation. The matrix-free solution to the equations, and Lagrangian advection of mesh-free nodes allowed for a fully parallelized implementation on the CPU and GPU, which ensured an affordable computing time and large time steps. A set of four benchmarks are presented to demonstrate the robustness and accuracy of the proposed formulation. The tested two- and three-dimensional simulations used Power Law, Casson and Bingham models. An Abram slump test and a dam break test were performed using the Bingham model, yielding visual and numerical results in accordance with the experimental data. A square lid-driven cavity was tested using the Casson model, while the Power Law model was used for a skewed lid-driven cavity test. The simulation results of the lid-driven cavity tests are in good agreement with velocity profiles and stream lines of published reports. A fully implicit scheme will be introduced in future work. As the method precisely reproduces the pressure field, non-Newtonian models that strongly depend on the pressure will be validated.