This paper presents a series of tests that have been conducted to validate the collision models of the HawkDSMC implementation. These tests cover the hard sphere (HS), variable hard sphere (VHS), and variable soft sphere (VSS) collision models, and the LarsenBorgnakke energy exchange model, for non-reacting gas mixtures. The results show that Hawkobtains the correct results in all cases under c...

Particle based methods for the description of hydrodynamic or fluid phenomena have attracted much interest during the last decade. Methods like the Multi-Particle Collision Dynamics method [1] (MPCD) or the Direct Simulation Monte Carlo method [2] (DSMC) represent schemes which close the gap between a purely microscopic description of matter, characterised by force fields, and a macroscopic con...

We will present some recent results about the development of numerical methods which are able to efficiently capture the multiscale aspects of some problems described by kinetic equations. In particular we will focus on fluid dynamics problems which present localized regions of departure from thermodynamical equilibrium. The basic idea, on which the methods rely, is to couple macroscopic hydrod...

We apply the Direct Simulation Monte Carlo (DSMC) method, developed originally to calculate rarefied gas dynamical problems, to study the gas flow in an accretion disc in a close binary system. The method involves viscosity and thermal conduction automatically, and can thus simulate turbulent viscosity (α viscosity).

combined residual modification with artificial neural network sign estimation to improve the prediction accuracy. Yao, et al [3] added an adaptive value in the grey differential equation to improve system performance. Su, Lin, and Hsu [4] proposed a Markov-Fourier grey model, in which Fourier series is used to fit residuals and Markov matrices is employed to encode possible global information g...

This research centers on laying the groundwork for the application of Bayesian statistical methods for the calibration of parameters relevant to modeling a hypersonic shock layer with the Direct Simulation Monte Carlo (DSMC) method. The DSMC method used in this work employs the algorithm of Bird (1994), with modifications to allow for the efficient simulation of a 1D hypersonic shock. The Larse...

Abstract To overcome the defects of traditional rarefied numerical methods such as Direct Simulation Monte Carlo (DSMC) method and unified Boltzmann equation schemes extend covering range macroscopic equations in high Knudsen number flows, data-driven nonlinear constitutive relations (DNCR) are proposed first through machine learning method. Based on training data from both Navier-Stokes (NS) s...

BACKGROUND Although interim analysis approaches in clinical trials are widely known, information on current practice of planned monitoring is still scarce. Reports of studies rarely include details on the strategies for both data monitoring and interim analysis. The aim of this project is to investigate the forms of monitoring used in cancer clinical trials and in particular to gather informati...