Two different kinetic models are used, coupled with heat transfer model, mass conservation equations, continuity equations and momentum equations.
The mass conservation law (continuity equation) and Darcy's law are two fundamental equations used in the numerical simulation.
Based on the above assumptions, the physical process of the supersonic molecular beam can be simulated by solving the combined equations of momentum conservation (N S), continuity, and energy conservation.
This leads to edge-based fluctuations in addition to the standard cell-based fluctuations, which are then distributed to the cell vertices in an upwind manner which retains the properties of the continuous scheme (positivity, linearity preservation, conservation, compactness and continuity).
The governing equations for mass continuity, momentum conservation, energy conservation and species conservation were discretized with the finite volume method (FVM).
The velocity in the wake was derived based on continuity conservation.
By setting minimum power consumption as optimization objective and entransy consumption as constraint condition, optimization flow field equation for convective heat transfer on the basis of energy conservation equation and continuity equation are constructed.
The method solves the two dimensional Naiver Stokes equations for conservation of momentum, continuity equation, and full nonlinear kinematic free-surface equation for Newtonian fluids, as the governing equations in a vertical plan.
The resulting shear band width is then compared with the minimum material flow layer thickness required for satisfying both mass conservation and velocity continuity conditions in a two-dimensional (2D) planar material flow around the tool pin.
Success of the semi-Lagrangian Vlasov model is enhanced by the good conservation of the continuity equation and stability of Maxwell system due to the fine description of the electron distribution function and particularly of the charge density and current density.
Equation (11) gives the fluid momentum equation with included effects of varying porosity and Eq. (12) is the conservation of mass (continuity) equation for an incompressible fluid in a porous medium.
