One-Dimensional Transient Radiative Transfer in Complex Semitransparent Medium by Meshless Method

2015 ◽  
Vol 29 (3) ◽  
pp. 610-619 ◽  
Author(s):  
Cheng-An Wang ◽  
Jian-Yu Tan
Keyword(s):  
Radiative Transfer ◽  
Meshless Method ◽  
One Dimensional ◽  
Semitransparent Medium

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

scholarly journals A global view of one-dimensional solar radiative transfer through oceanic water clouds

2010 ◽  
Vol 37 (18) ◽  
pp. n/a-n/a ◽  
Author(s):  
Larry Di Girolamo ◽  
Lusheng Liang ◽  
Steven Platnick
Keyword(s):  
Radiative Transfer ◽  
Oceanic Water ◽  
One Dimensional ◽  
Global View

scholarly journals Atmospheric Escape and the Evolution of Close-In Exoplanets

2019 ◽  
Vol 47 (1) ◽  
pp. 67-90 ◽  
Author(s):  
James E. Owen
Keyword(s):  
Radiative Transfer ◽  
Lower Mass ◽  
Hydrodynamic Simulations ◽  
One Dimensional ◽  
Hot Jupiters ◽  
Atmospheric Escape ◽  
Hydrodynamic Calculations ◽  
Ionization Chemistry ◽  
Exoplanet Systems ◽  
Over Time

Exoplanets with substantial hydrogen/helium atmospheres have been discovered in abundance, many residing extremely close to their parent stars. The extreme irradiation levels that these atmospheres experience cause them to undergo hydrodynamic atmospheric escape. Ongoing atmospheric escape has been observed to be occurring in a few nearby exoplanet systems through transit spectroscopy both for hot Jupiters and for lower-mass super-Earths and mini-Neptunes. Detailed hydrodynamic calculations that incorporate radiative transfer and ionization chemistry are now common in one-dimensional models, and multidimensional calculations that incorporate magnetic fields and interactions with the interstellar environment are cutting edge. However, comparison between simulations and observations remains very limited. While hot Jupiters experience atmospheric escape, the mass-loss rates are not high enough to affect their evolution. However, for lower-mass planets, atmospheric escape drives and controls their evolution, sculpting the exoplanet population that we observe today. ▪ Observations of some exoplanets have detected atmospheric escape driven by hydrodynamic outflows, causing the exoplanets to lose mass over time. ▪ Hydrodynamic simulations of atmospheric escape are approaching the sophistication required to compare them directly to observations. ▪ Atmospheric escape sculpts sharp features into the exoplanet population that we can observe today; these features have recently been detected.

Radiative transfer in a one-dimensional fluctuating albedo mixture

1994 ◽  
Author(s):  
Daniel Vanderhaegen ◽  
Claude Deutsch ◽  
Patrick Boissé
Keyword(s):  
Radiative Transfer ◽  
One Dimensional

scholarly journals Understanding nebular spectra of Type Ia supernovae

2020 ◽  
Vol 494 (2) ◽  
pp. 2221-2235 ◽  
Author(s):  
Kevin D Wilk ◽  
D John Hillier ◽  
Luc Dessart
Keyword(s):  
Radiative Transfer ◽  
Local Thermodynamic Equilibrium ◽  
Diagnostic Feature ◽  
Type Ia Supernovae ◽  
Thermal Heating ◽  
One Dimensional ◽  
Type Ia ◽  
Natural Mechanism ◽  
Non Local ◽  
Ia Supernovae

ABSTRACT In this study, we present one-dimensional, non-local-thermodynamic-equilibrium, radiative transfer simulations (using cmfgen) in which we introduce micro-clumping at nebular times into two Type Ia supernova ejecta models. We use one sub-Chandrasekhar (sub-MCh) ejecta model with 1.04 M⊙ and one Chandrasekhar (MCh) ejecta model with 1.40 M⊙. We introduce clumping factors f = 0.33, 0.25, and 0.10, which are constant throughout the ejecta, and compare results to the unclumped f = 1.0 case. We find that clumping is a natural mechanism to reduce the ionization of the ejecta, reducing emission from [Fe iii], [Ar iii], and [S iii] by a factor of a few. For decreasing values of the clumping factor f, the [Ca ii] λλ7291,7324 doublet became a dominant cooling line for our MCh model but remained weak in our sub-MCh model. Strong [Ca ii] λλ7291,7324 indicates non-thermal heating in that region and may constrain explosion modelling. Due to the low abundance of stable nickel, our sub-MCh model never showed the [Ni ii] 1.939-μm diagnostic feature for all clumping values.

The SKN Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Isotropically Scattering Plane-Parallel Medium: Part 1

2002 ◽  
Vol 124 (4) ◽  
pp. 674-684 ◽  
Author(s):  
Zekeriya Altac¸
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Differential Equations ◽  
Order Approximation ◽  
High Order ◽  
High Order Approximation ◽  
One Dimensional ◽  
Second Order Differential Equations ◽  
Plane Parallel ◽  
Transfer Problems

A high order approximation, the SKN method—a mnemonic for synthetic kernel—is proposed for solving radiative transfer problems in participating medium. The method relies on approximating the integral transfer kernel by a sum of exponential kernels. The radiative integral equation is then reducible to a set of coupled second-order differential equations. The method is tested for one-dimensional plane-parallel participating medium. Three quadrature sets are proposed for the method, and the convergence of the method with the proposed sets is explored. The SKN solutions are compared with the exact, PN, and SN solutions. The SK1 and SK2 approximations using quadrature Set-2 possess the capability of solving radiative transfer problems in optically thin systems.

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