17,957 research outputs found
Space-Angle Discontinuous Galerkin Finite Element Method for Radiative Transfer Equation
Radiative transfer theory describes the interaction of radiation with scattering and absorbing media. It has applications in neutron transport, atmospheric physics, heat transfer, molecular imaging, and others. In steady state, the radiative transfer equation is an integro-differential equation of five independent variables, which are 3 dimensions in space and 2 dimensions in the angular direction. This high dimensionality and the presence of the integral term present serious challenges when solving the equation numerically. Over the past 50 years, several techniques for solving the radiative transfer equation (RTE) have been introduced. These include, but are certainly not limited to, Monte Carlo methods, discrete-ordinate methods, spherical harmonics methods, spectral methods, finite difference methods, and finite element methods. Methods involving discrete ordinates and spherical harmonics have received particular attention in the literature.
This work introduces a parallel space-angle discontinuous Galerkin (saDG) method to solve the steady-state RTEs. The objective-oriented design of the software allowed us to apply the saDG approach to a variety of RTEs with considerable ease, including 1x1s, 1x2s, and 2x2s. The direct solver can achieve high-order accuracy solutions for low-dimensional problems. However, for high-dimensional problems, the direct solver is time-consuming and requires significant memory usage that may exceed the computer\u27s RAM capacity. To address this issue, we employed the Angular Decomposition (AD) method in the iterative solver, which improves runtime efficiency and reduces memory usage. To handle large-scale problems, we developed a parallel solver based on AD and Domain Decomposition (DD) methods. Finally, we applied Reflective Boundary Conditions to 2-D Cartesian radiative transfer problems
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Rarefied flow between plates of finite length via the coupling approach
This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The coexistence of rarefied continuum flow regime areas and relatively small elements in which rarefaction effects become important is a typical feature of many complex gas flows micro systems. In rarefied domains, the mean free path of gas molecules is comparable or larger than a characteristic scale of the system. These domains are naturally described by kinetic equation for the velocity distribution function, which involve a considerable effort in terms of CPU time and memory requirements, due to the discretization in both physical and velocity space. The continuum domains are best described by the fluid Navier Stokes (NS) equations in terms of average flow velocity, gas density and temperature. These equations are more efficient, but less accurate in critical rarefied areas. Thus, the development of hybrid solver combining kinetic and continuum models is of great interest especially for applications range from gas flows in micro systems to the aerospace applications, such as high altitude flights. The pressure–driven gas flow of rarified monatomic gas through a two-dimensional short microchannel is considered using hybrid solver. The calculations have been carried out for pressure ratios 0.1, 0.5 and 0.9 and fixed relatively large Knudsen number. The applicability of the solver is discussed via comparison with the kinetic and NS solutions.The European Community's Seventh Framework Programme FP7/2007-2013 under grant agreement ITN GASMEMS no 215504
A Hierarchy of Hybrid Numerical Methods for Multi-Scale Kinetic Equations
In this paper, we construct a hierarchy of hybrid numerical methods for
multi-scale kinetic equations based on moment realizability matrices, a concept
introduced by Levermore, Morokoff and Nadiga. Following such a criterion, one
can consider hybrid scheme where the hydrodynamic part is given either by the
compressible Euler or Navier-Stokes equations, or even with more general
models, such as the Burnett or super-Burnett systems.Comment: 27 pages, edit: typo and metadata chang
A Multiscale Kinetic-Fluid Solver with Dynamic Localization of Kinetic Effects
This paper collects the efforts done in our previous works [P. Degond, S.
Jin, L. Mieussens, A Smooth Transition Between Kinetic and Hydrodynamic
Equations, J. Comp. Phys., 209 (2005) 665--694.],[P.Degond, G. Dimarco, L.
Mieussens, A Moving Interface Method for Dynamic Kinetic-fluid Coupling, J.
Comp. Phys., Vol. 227, pp. 1176-1208, (2007).],[P. Degond, J.G. Liu, L.
Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects,
SIAM Multi. Model. Sim. 5(3), 940--979 (2006)] to build a robust multiscale
kinetic-fluid solver. Our scope is to efficiently solve fluid dynamic problems
which present non equilibrium localized regions that can move, merge, appear or
disappear in time. The main ingredients of the present work are the followings
ones: a fluid model is solved in the whole domain together with a localized
kinetic upscaling term that corrects the fluid model wherever it is necessary;
this multiscale description of the flow is obtained by using a micro-macro
decomposition of the distribution function [P. Degond, J.G. Liu, L. Mieussens,
Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi.
Model. Sim. 5(3), 940--979 (2006)]; the dynamic transition between fluid and
kinetic descriptions is obtained by using a time and space dependent transition
function; to efficiently define the breakdown conditions of fluid models we
propose a new criterion based on the distribution function itself. Several
numerical examples are presented to validate the method and measure its
computational efficiency.Comment: 34 page
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