The continuity equation (9.48) contains the three unknowns n(2), J, and j. It is reduced to an equation involving the single unknown n(2) when alternative expressions are available for J and j in terms of n(2). The expression (9.48) is the most general configuration information (within...
The unknown distribution population at a wall node which is necessary to fulfill streaming step is decomposed into its equilibrium and non-equilibrium parts. The equilibrium part is evaluated according to Dirichlet and Neumann boundary constraints, and the non-equilibrium part is obtained using a ...
When there are frequent collisions, the particle comes to a limiting velocity proportional to E. The electrons in a copper wire, for instance, drift together with a velocity \rm v=\mu E , where \mu is the mobility. A magnetic field also limits free-streaming by forcing particles to ...
It is common, in uncertainty quantification works [1], [33], [47], [53], [63], [92], [102], to emphasize the fact a quantity is uncertain by introducing explicitly an additional dependence to the unknown of interest with respect to an uncertain parameter (a stochastic process) here ...
Remark For a unique line, ξξ, ηη, and ζζ are defined up to a constant nonzero multiple. The equation (2) says that the vector of these coefficients is an eigenvector of M(x,y)M(x,y) associated with the zero eigenvalue. So for a unique line, we need that the corresponding...
The unknown distribution population at a wall node which is necessary to fulfill streaming step is decomposed into its equilibrium and non-equilibrium parts. The equilibrium part is evaluated according to Dirichlet and Neumann boundary constraints, and the non-equilibrium part is obtained using a ...
After the streaming step, the temperature distribution functions at the fluid node nearest to the wall are unknown. To calculate the unknown distributions, an interpolation scheme is used: 𝑔𝑖(𝑥⃗𝑓,𝑡+Δ𝑡)=11+2Δ−𝛾𝑔𝑖(𝑥⃗𝑟′,𝑡+Δ𝑡)+2Δ−𝛾1+2Δ...
After the streaming step, the temperature distribution functions at the fluid node nearest to the wall are unknown. To calculate the unknown distributions, an interpolation scheme is used: 𝑔𝑖(𝑥⃗𝑓,𝑡+Δ𝑡)=11+2Δ−𝛾𝑔𝑖(𝑥⃗𝑟′,𝑡+Δ𝑡)+2Δ−𝛾1+2Δ...