10,519 research outputs found
A radiation-hydrodynamics scheme valid from the transport to the diffusion limit
We present in this paper the numerical treatment of the coupling between
hydrodynamics and radiative transfer. The fluid is modeled by classical
conservation laws (mass, momentum and energy) and the radiation by the grey
moment system. The scheme introduced is able to compute accurate
numerical solution over a broad class of regimes from the transport to the
diffusive limits. We propose an asymptotic preserving modification of the HLLE
scheme in order to treat correctly the diffusion limit. Several numerical
results are presented, which show that this approach is robust and have the
correct behavior in both the diffusive and free-streaming limits. In the last
numerical example we test this approach on a complex physical case by
considering the collapse of a gas cloud leading to a proto-stellar structure
which, among other features, exhibits very steep opacity gradients.Comment: 29 pages, submitted to Journal of Computational physic
On Iterative Algorithms for Quantitative Photoacoustic Tomography in the Radiative Transport Regime
In this paper, we describe the numerical reconstruction method for
quantitative photoacoustic tomography (QPAT) based on the radiative transfer
equation (RTE), which models light propagation more accurately than diffusion
approximation (DA). We investigate the reconstruction of absorption coefficient
and/or scattering coefficient of biological tissues. Given the scattering
coefficient, an improved fixed-point iterative method is proposed to retrieve
the absorption coefficient for its cheap computational cost. And we prove the
convergence. To retrieve two coefficients simultaneously, Barzilai-Borwein (BB)
method is applied. Since the reconstruction of optical coefficients involves
the solution of original and adjoint RTEs in the framework of optimization, an
efficient solver with high accuracy is improved from~\cite{Gao}. Simulation
experiments illustrate that the improved fixed-point iterative method and the
BB method are the comparative methods for QPAT in two cases.Comment: 21 pages, 44 figure
Flux-Limited Diffusion for Multiple Scattering in Participating Media
For the rendering of multiple scattering effects in participating media,
methods based on the diffusion approximation are an extremely efficient
alternative to Monte Carlo path tracing. However, in sufficiently transparent
regions, classical diffusion approximation suffers from non-physical radiative
fluxes which leads to a poor match to correct light transport. In particular,
this prevents the application of classical diffusion approximation to
heterogeneous media, where opaque material is embedded within transparent
regions. To address this limitation, we introduce flux-limited diffusion, a
technique from the astrophysics domain. This method provides a better
approximation to light transport than classical diffusion approximation,
particularly when applied to heterogeneous media, and hence broadens the
applicability of diffusion-based techniques. We provide an algorithm for
flux-limited diffusion, which is validated using the transport theory for a
point light source in an infinite homogeneous medium. We further demonstrate
that our implementation of flux-limited diffusion produces more accurate
renderings of multiple scattering in various heterogeneous datasets than
classical diffusion approximation, by comparing both methods to ground truth
renderings obtained via volumetric path tracing.Comment: Accepted in Computer Graphics Foru
Unified Gas-kinetic Wave-Particle Methods III: Multiscale Photon Transport
In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method
to the multiscale photon transport. In this method, the photon free streaming
and scattering processes are treated in an un-splitting way. The duality
descriptions, namely the simulation particle and distribution function, are
utilized to describe the photon. By accurately recovering the governing
equations of the unified gas-kinetic scheme (UGKS), the UGKWP preserves the
multiscale dynamics of photon transport from optically thin to optically thick
regime. In the optically thin regime, the UGKWP becomes a Monte Carlo type
particle tracking method, while in the optically thick regime, the UGKWP
becomes a diffusion equation solver. The local photon dynamics of the UGKWP, as
well as the proportion of wave-described and particle-described photons are
automatically adapted according to the numerical resolution and transport
regime. Compared to the -type UGKS, the UGKWP requires less memory cost
and does not suffer ray effect. Compared to the implicit Monte Carlo (IMC)
method, the statistical noise of UGKWP is greatly reduced and computational
efficiency is significantly improved in the optically thick regime. Several
numerical examples covering all transport regimes from the optically thin to
optically thick are computed to validate the accuracy and efficiency of the
UGKWP method. In comparison to the -type UGKS and IMC method, the UGKWP
method may have several-order-of-magnitude reduction in computational cost and
memory requirement in solving some multsicale transport problems.Comment: 27 pages, 15 figures. arXiv admin note: text overlap with
arXiv:1810.0598
Asymptotic-Preserving Monte Carlo methods for transport equations in the diffusive limit
We develop a new Monte Carlo method that solves hyperbolic transport
equations with stiff terms, characterized by a (small) scaling parameter. In
particular, we focus on systems which lead to a reduced problem of parabolic
type in the limit when the scaling parameter tends to zero. Classical Monte
Carlo methods suffer of severe time step limitations in these situations, due
to the fact that the characteristic speeds go to infinity in the diffusion
limit. This makes the problem a real challenge, since the scaling parameter may
differ by several orders of magnitude in the domain. To circumvent these time
step limitations, we construct a new, asymptotic-preserving Monte Carlo method
that is stable independently of the scaling parameter and degenerates to a
standard probabilistic approach for solving the limiting equation in the
diffusion limit. The method uses an implicit time discretization to formulate a
modified equation in which the characteristic speeds do not grow indefinitely
when the scaling factor tends to zero. The resulting modified equation can
readily be discretized by a Monte Carlo scheme, in which the particles combine
a finite propagation speed with a time-step dependent diffusion term. We show
the performance of the method by comparing it with standard (deterministic)
approaches in the literature
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