We develop a consistent discretization of conservative momentum and scalar transport for the numerical simulation of flow using a generalized moving curvilinear coordinate system. The formulation guarantees consistency between the discrete transport equation and the discrete mass conservation equation due to grid motion. This enables simulation of conservative transport using generalized curvil...

Modeling subsurface solute transport is difficult-more so than modeling heads and flows. The classical governing equation does not always adequately represent what we see at the field scale. In such cases, commonly used numerical models are solving the wrong equation. Also, the transport equation is hyperbolic where advection is dominant, and parabolic where hydrodynamic dispersion is dominant....

This paper is devoted to the derivation of a macroscopic diffusion equation (Fourier’s law) describing the transport of energy in an anharmonic chain. More precisely, we study here the so-called FPU-β chain, which is a very simple model for a one-dimensional crystal in which atoms are coupled to their nearest neighbors by a harmonic potential, weakly perturbed by a quartic potential. The starti...

We propose a rigorous procedure to obtain the adjoint-based gradient representation of cost functionals for the optimal control of discontinuous solutions of conservation laws. Hereby, it is not necessary to introduce adjoint variables for the shock positions. Our approach is based on stability properties of the adjoint equation. We give a complete analysis for the case of convex scalar conserv...

The problem of global illumination in computer graphics is described by a second kind Fredholm integral equation Due to the com plexity of this equation Monte Carlo methods provide an interesting tool for approximating solutions to this transport equation For the case of the radiosity equation we present the deterministic method of quasi random walks This method very e ciently uses low discrepa...

This paper presents a new dynamic one equation eddy viscosity model for LES of compressible flows. Based on the compressible version of dynamic Smagorinsky model (DSM), the transport equation for sub-grid scale (SGS) kinetic energy (KE) is introduced to predict SGS KE, instead of the commonly used Yoshizawa’s model. The SGS KE transport equation for compressible flow is derived, and the unclose...

Biological tissue scatters light mainly in the forward direction where the scattering phase function has a narrow peak. This peak makes it difficult to solve the radiative transport equation. However, it is just for forward-peaked scattering that the Fokker-Planck equation provides a good approximation, and it is easier to solve than the transport equation. Furthermore, the modification of the ...

This paper presents a formal exact solution of the linear advection–diffusion transport equation with constant coefficients for both transient and steady-state regimes. A classical mathematical substitution transforms the original advection–diffusion equation into an exclusively diffusive equation. The new diffusive problem is solved analytically using the classic version of Generalized Integra...

In this paper the interaction of attosecond laser pulses with matter is investigated. The scattering and potential motion of heat carriers as well as the external force are considered. Depending on the ratio of the scatterings and potential motion the heat transport is described by the thermal forced Klein-Gordon or thermal modified telegraph equation. For thermal Heisenberg type relation V τ ∼...