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Fujihiro Hamba  One of the best experts on this subject based on the ideXlab platform.

analysis of destruction term in Transport Equation for turbulent energy dissipation rate
Theoretical and Computational Fluid Dynamics, 2019CoAuthors: Fujihiro Hamba, Kouta KanamotoAbstract:The K–\(\varepsilon \) model used in turbulence simulations involves the Transport Equations for the turbulent kinetic energy and its dissipation rate. In contrast to the turbulent energy Equation derived from the Navier–Stokes Equation, the Transport Equation for the dissipation rate has been modeled empirically and has less of a theoretical grounding. An analysis of the dependence of terms in the exact Transport Equation on the Reynolds number \(\textit{Re}\) has suggested that the two dominant \(O(\textit{Re}^{1/2})\) terms cancel out at the leading order and their O(1) difference yields the terms in the model Equation. The twoscale direct interaction approximation (TSDIA) can be used to derive the model Equation for inhomogeneous turbulence. In this study, as a first step toward deriving all the terms in the model Equation, the two dominant terms in the exact Transport Equation were investigated theoretically and numerically for the case of homogeneous isotropic turbulence, in order to derive the destruction term. The two terms were first analyzed by using the TSDIA under the assumption of a simple energy spectrum form. However, the finitewidth effect of the inertial range of the energy spectrum did not give the expected \(O(\textit{Re}^{1/2})\) corrections to the leadingorder terms. Then, the model Equations of the Markovianized Lagrangian renormalized approximation (MLRA) were numerically solved to obtain the accurate energy spectrum profile of a decaying homogeneous isotropic turbulence. Thereby, it was shown that the deviation of the energy spectrum from the \(5/3\) law was responsible for the \(O(\textit{Re}^{1/2})\) corrections. By assuming the energy spectrum suggested by the MLRA results, the two dominant terms were analyzed again by using the TSDIA to successfully derive the destruction term in the model Equation.

turbulent energy density and its Transport Equation in scale space
Physics of Fluids, 2015CoAuthors: Fujihiro HambaAbstract:The energy spectrum contains information not only on the intensity but also on the scale dependence of the turbulent fluctuations; the spectrum is commonly used to describe the dynamics of homogeneous isotropic turbulence. On the other hand, onepoint statistical quantities such as the turbulent kinetic energy are mainly treated for inhomogeneous turbulence. Although the energy spectrum must be useful in describing the scale dependence of inhomogeneous turbulence, the Fourier transform cannot be performed in general cases. In this work, instead of the energy spectrum in the wavenumber space, the energy density in the scale space was introduced on the basis of the twopoint velocity correlation in the physical space. The Transport Equation for the energy density was derived for inhomogeneous turbulence. Direct numerical simulation (DNS) data of homogeneous isotropic turbulence were first used to evaluate the energy transfer in the scale space. The energy density Equation was compared with the energy spectrum Equation to assess the role of the energy density. DNS data of turbulent channel flow were also used to evaluate the energy density Equation for inhomogeneous turbulence. The energy Transport in the physical and scale spaces was examined in different regions of channel flow. It was shown that the Transport Equation for the energy density adequately describes the energy transfer in the scale space. The energy flux from the large to the small scales was observed for both turbulent flows in a similar manner to the conventional energy cascade in the wavenumber space.

exact Transport Equation for eddy diffusivity in turbulent shear flow
Theoretical and Computational Fluid Dynamics, 2013CoAuthors: Fujihiro HambaAbstract:TwoEquation models that treat the Transport Equations for two variables are typical models for the Reynoldsaveraged Navier–Stokes Equation. Compared to the Equation for the turbulent kinetic energy, the Equation for the second variable such as the dissipation rate does not have a theoretical analogue. In this work, the exact Transport Equation for the eddy diffusivity was derived and examined for better understanding turbulence and improving twoEquation models. A new length scale was first introduced, which involves the response function for the scalar fluctuation. It was shown that the eddy diffusivity can be expressed as the correlation between the velocity fluctuation and the new length scale. The Transport Equations for the eddy diffusivity and the lengthscale variance were derived theoretically. Statistics such as terms in the Transport Equations were evaluated using the direct numerical simulation of turbulent channel flow. It was shown that the streamwise component of the eddy diffusivity is greater than the other two components in the whole region. In the Transport Equation for the eddy diffusivity, the production term due to the Reynolds stress is a main positive term, whereas the pressure–lengthgradient correlation term plays a role of destruction. It is expected that the analysis of the Transport Equations is helpful in developing better turbulence models.
Randal S Baker  One of the best experts on this subject based on the ideXlab platform.

a block adaptive mesh refinement algorithm for the neutral particle Transport Equation
Nuclear Science and Engineering, 2002CoAuthors: Randal S BakerAbstract:We describe the development and implementation of a blockbased adaptive mesh refinement (AMR) algorithm for solving the discrete ordinates neutral particle Transport Equation. AMR algorithms allow mesh refinement in areas of interest without requiring the extension of this refinement throughout the entire problem geometry, minimizing the number of computational cells required for calculations. The blockbased AMR algorithm described here is a hybrid between traditional cell or patchbased approaches and is designed to allow an efficient parallel solution of the Transport Equation while still reducing the cell count. This paper discusses the data structure implementation and CPU/memory efficiency for our Block AMR method, the Equations and procedures used in mapping edge fluxes between blocks of different refinement levels for both diamond and linear discontinuous spatial discretizations, effects of AMR on mesh convergence, and our approach to parallelization. Comparisons between our Block AMR method and a traditional singlelevel mesh are presented for a sample brachytherapy problem. The Block AMR results are shown to be significantly faster for this problem (on at least a few processors), while still returning an accurate solution.

a block adaptive mesh refinement algorithm for the neutral particle Transport Equation
Nuclear Science and Engineering, 2002CoAuthors: Randal S BakerAbstract:We describe the development and implementation of a blockbased adaptive mesh refinement (AMR) algorithm for solving the discrete ordinates neutral particle Transport Equation. AMR algorithms allow...
Yan Guo  One of the best experts on this subject based on the ideXlab platform.

geometric correction for diffusive expansion of steady neutron Transport Equation
Communications in Mathematical Physics, 2015CoAuthors: Yan GuoAbstract:We revisit the diffusive limit of a steady neutron Transport Equation in a twodimensional unit disk with onespeed velocity. A classical theorem by Bensoussan et al. (Publ Res Inst Math Sci 15(1):53–157, 1979) states that its solution can be approximated in L∞ by the leading order interior solution plus the Knudsen layer in the diffusive limit. In this paper, we construct a counterexample to this result via a different boundary layer expansion with geometric correction.

geometric correction for diffusive expansion of steady neutron Transport Equation
arXiv: Analysis of PDEs, 2014CoAuthors: Yan GuoAbstract:We revisit the diffusive limit of a steady neutron Transport Equation in a $2$D unit disk with onespeed velocity. We show the classical result in [4] with Milne expansion is incorrect in $L^{\infty}$ and we give the right answer in studying the $\epsilon$Milne expansion with geometric correction.
John C Schotland  One of the best experts on this subject based on the ideXlab platform.

ultrasound modulated bioluminescence tomography and controllability of the radiative Transport Equation
Siam Journal on Mathematical Analysis, 2016CoAuthors: Francis J Chung, John C SchotlandAbstract:We propose a method to reconstruct the density of an optical source in a highly scattering medium from ultrasound modulated optical measurements. Our approach is based on the solution to a hybrid inverse source problem for the radiative Transport Equation (RTE). A controllability result for the RTE plays an essential role in the analysis.

ultrasound modulated bioluminescence tomography and controllability of the radiative Transport Equation
Siam Journal on Mathematical Analysis, 2016CoAuthors: Guillaume Bal, Francis J Chung, John C SchotlandAbstract:We propose a method to reconstruct the density of an optical source in a highly scattering medium from ultrasound modulated optical measurements. Our approach is based on the solution to a hybrid inverse source problem for the radiative Transport Equation (RTE). A controllability result for the RTE plays an essential role in the analysis.

the green s function for the radiative Transport Equation in the slab geometry
Journal of Physics A, 2010CoAuthors: Manabu Machida, John C Schotland, George Y Panasyuk, Vadim A MarkelAbstract:The radiative Transport Equation is solved in the threedimensional slab geometry by means of the method of rotated reference frames. In this spectral method, the solution is expressed in terms of analytical functions such as spherical harmonics and Wigner dfunctions. In addition, the eigenvalues and eigenvectors of a tridiagonal matrix and certain coefficients, which are determined from the boundary conditions, must also be computed. The Green's function for the radiative Transport Equation is computed and the results are compared with diffusion approximation and Monte Carlo simulations. We find that the diffusion approximation is not quite correct inside the slab, even when the light emitted from the slab is well described by the diffusion approximation. The solutions we obtain are especially convenient for solving inverse problems associated with radiative Transport.

fourier laplace structure of the inverse scattering problem for the radiative Transport Equation
Inverse Problems and Imaging, 2007CoAuthors: John C Schotland, Vadim A MarkelAbstract:We consider the inverse scattering problem for the radiative trans port Equation. We show that the linearized form of this problem can be formu lated in terms of the inversion of a suitably defined FourierLaplace transform. This generalizes a previous result obtained within the diffusion approximation to the radiative Transport Equation.

radiative Transport Equation in rotated reference frames
arXiv: Mathematical Physics, 2005CoAuthors: George Y Panasyuk, John C Schotland, Vadim A MarkelAbstract:A novel method for solving the linear radiative Transport Equation (RTE) in a threedimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(s,s') with the constraint that it depends only on the angle between the angular variables s and s'. This corresponds to spherically symmetric (on average) random medium constituents. Boundary conditions are considered in the slab and halfspace geometries. The approach developed in this paper is spectral. It allows for the expansion of the solution to the RTE in terms of analytical functions of angular and spatial variables to relatively high orders. The coefficients of this expansion must be computed numerically. However, the computational complexity of this task is much smaller than in the standard method of spherical harmonics. The solutions obtained are especially convenient for solving inverse problems associated with radiative transfer.
Dumitru Baleanu  One of the best experts on this subject based on the ideXlab platform.

solution of a fractional Transport Equation by using the generalized quadratic form
Communications in Nonlinear Science and Numerical Simulation, 2011CoAuthors: Abdelouhab Kadem, Dumitru BaleanuAbstract:Abstract In this manuscript the one dimensional fractional Transport Equation in which the prescribed source and angular flux are spatially quadratic is investigated within the generalized quadratic form method. It is reported that the angular flux satisfies Fick’s law and the corresponding scalar flux satisfies the fractional generalization of the classic diffusion Equation.

analytical method based on walsh function combined with orthogonal polynomial for fractional Transport Equation
Communications in Nonlinear Science and Numerical Simulation, 2010CoAuthors: Abdelouhab Kadem, Dumitru BaleanuAbstract:Abstract In this paper a novel method based on Walsh function combined with a Chebyshev polynomials of the first kind was applied for the resolution of fractional Transport Equation in threedimensions. A specific application of the method is discussed.