An Integral Formulation of Transient Radiative Transfer

2000 ◽  
Vol 123 (3) ◽  
pp. 466-475 ◽  
Author(s):  
Z.-M. Tan ◽  
P.-F. Hsu
Keyword(s):  
Radiative Transfer ◽  
Incident Radiation ◽  
Integral Formulation ◽  
Time Dependent ◽  
Slab Geometry ◽  
Time Step ◽  
Participating Media ◽  
Quadrature Methods ◽  
Time Dependent Domain ◽  
Large Time Step

A time-dependent integral formulation is developed for modeling transient radiative transfer. The development is based on a rigorous analysis of the wave propagation process inside the participating media. The physical significance of the present integral formulation is the consideration of the time-dependent domain of computation, which is different from the domain disturbed by radiation (i.e., the wave front envelope). Numerical computations are performed for the medium that is an absorbing and isotropically scattering one-dimensional plane slab geometry. The spatial and temporal incident radiation and radiative flux distributions are presented for different boundary conditions and for uniform and nonuniform property distribution. The transient results at large time step are compared with steady-state solutions by the finite volume and quadrature methods and show excellent agreement. The solutions of reflecting boundary condition exhibit distinctive behavior from that of the non-reflecting boundary.

Numerical Results of an Integral Formulation of Transient Radiative Transfer

1999 ◽  
Author(s):  
Z.-M. Tan ◽  
P.-F. Hsu
Keyword(s):  
Steady State ◽  
Radiative Transfer ◽  
Incident Radiation ◽  
Integral Formulation ◽  
Time Step ◽  
Incident Intensity ◽  
Participating Media ◽  
Upwind Difference Scheme ◽  
The One ◽  
Reflecting Surface

Abstract Numerical computations are performed for the transient radiative transfer equation within the one-dimensional parallel plate geometry using an integral formulation obtained in a prior work. The medium under consideration is absorbing and isotropically scattering. One boundary is a black emitting surface or a transparent surface subjected to the collimated incident radiation. The incident intensity is applied at the start of the transient. The other boundary is a cold and black or specularly reflecting surface. The spatial and temporal incident radiation and radiative flux distributions are presented for different boundary conditions and for uniform and nonuniform property distribution. The transient results at large time step are compared with steady-state solutions by the finite volume and quadrature methods and show excellent agreement. The solutions of reflecting boundary condition exhibit distinctive behavior from that of the non-reflecting boundary. The integral formulation is extended to handle the transient transfer within the nonhomogeneous participating media. The integral formulation has several advantages over the differential treatment of the hyperbolic wave of the radiative transport; among others: (1) The avoidance of using a high order upwind difference scheme in resolving the wave front; (2) Providing a sound basis for physical interpretation as the radiative transfer is a volumetric process; and (3) Many integral equation numerical methods that have previously been developed for the steady state integral formulation can be re-applied to treat the transient problem.

Transient Radiation Coupled With Conduction Heat Transfer in a One Dimensional Slab

2014 ◽  
Vol 619 ◽  
pp. 94-98
Author(s):  
Prerana Nashine ◽  
Ashok Kumar Satapathy
Keyword(s):  
Radiative Transfer ◽  
Radiation Effects ◽  
Research Work ◽  
Incident Radiation ◽  
Time Step ◽  
Participating Media ◽  
Transient Radiation ◽  
Transfer Equations ◽  
Volume Method ◽  
Radiative Transfer Equations

The present research work views over a solution of radiative transport problem along with conduction in one perspective piece and in the existence of participating media. The radiative transfer equations are developed for anisotropically scattering, absorbing, emitting medium and the equation is being discretized using finite volume method. Heat flux and the incident radiation effects have been computed at three different time step. Transient radiation along with transient conduction is solved and the radiative effect has been measured using radiative transfer equation while the conduction term has been measured using conduction equation.

The Solution of Transient Radiative Transfer With Collimated Incident Serial Pulse in a Plane-Parallel Medium by the DRESOR Method

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
Qiang Cheng ◽  
Huai-Chun Zhou ◽  
Zhi-Feng Huang ◽  
Yong-Lin Yu ◽  
De-Xiu Huang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Transfer ◽  
Incident Radiation ◽  
Anisotropic Scattering ◽  
Time Dependent ◽  
Temporal Response ◽  
One Dimensional ◽  
Unit Energy ◽  
The Monte Carlo Method

A time-dependent distribution of ratios of energy scattered by the medium or reflected by the boundary surfaces (DRESOR) method was proposed to solve the transient radiative transfer in a one-dimensional slab. This slab is filled with an absorbing, scattering, and nonemitting medium and exposed to a collimated, incident serial pulse with different pulse shapes and pulse widths. The time-dependent DRESOR values, representing the temporal response of an instantaneous, incident pulse with unit energy and the same incident direction as that for the serial pulse, were proposed and calculated by the Monte Carlo method. The temporal radiative intensity inside the medium with high directional resolution can be obtained from the time-dependent DRESOR values. The transient incident radiation results obtained by the DRESOR method were compared to those obtained with the Monte Carlo method, and good agreements were achieved. Influences of the pulse shape and width, reflectivity of the boundary, scattering albedo, optical thickness, and anisotropic scattering on the transient radiative transfer, especially the temporal response along different directions, were investigated.

Efficient numerical treatment of nonlinearities in the advection–diffusion–reaction equations

2019 ◽  
Vol 29 (1) ◽  
pp. 132-145
Author(s):  
Utku Erdogan ◽  
Murat Sari ◽  
Huseyin Kocak
Keyword(s):  
Large Time ◽  
Newton Iteration ◽  
Time Dependent ◽  
Diffusion Reaction ◽  
Time Step ◽  
Content Type ◽  
Advection Diffusion ◽  
Large Time Step ◽  
Reaction Equations ◽  
Advection Diffusion Reaction Equations

Purpose The purpose of this study is to propose a non-classical method to obtain efficient and accurate numerical solutions of the advection–diffusion–reaction equations. Design/methodology/approach Unlike conventional numerical methods, this study proposes a numerical scheme using outer Newton iteration applied to a time-dependent PDE. The linearized time dependent PDE is discretized by trapezoidal rule, which is second order in time, and by spline-based finite difference method of fourth order in space. Findings Using the proposed technique, even when relatively large time step sizes are used in computations, the efficiency of the proposed procedure is very clear for the numerical examples in comparison with the existing classical methods. Originality/value This study, unlike these classical methods, proposes an alternative approach based on linearizing the nonlinear problem at first, and then discretizing it by an appropriate scheme. This technique helps to avoid considering the convergence issues of Newton iteration applied to nonlinear algebraic system containing many unknowns at each time step if an implicit method is used in time discretization. The linearized PDE can be solved by implicit time integrator, which enables the use of large time step size.

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

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