The proposed model considers the unsteady friction term and comprises the continuity and momentum conserve equations, which are solved by the method of characteristics.
Fluids 8 (1965) 2182 2189] introduced a discretization method for the incompressible Navier Stokes equations conserving the secondary quantities kinetic energy and vorticity, besides the primary quantities mass and momentum.
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The functionals (E v)) and (F v)) defined above are conserved quantities under equation (2.1).
Thus, the motion still lies in a plane perpendicular to L and the magnitude is conserved, from the equation.
Maxwell's equations conserve certain properties the magnetic field intensity, the electric displacement field and the Poynting vector that describes the electric flux of an electromagnetic field.
Similarly, one can show that the variance 〈 N ˆ 2 〉 of the total particle number is also conserved exactly by equations (4) and (5).
We describe an energy enstrophy conserving discretisation for the rotating shallow water equations with slip boundary conditions.
The model is a coupled system that consists of incompressible Navier Stokes equations with a generalized Navier boundary condition and Cahn Hilliard equation in conserved form.
In particular, the nonautonomous difference equation (77) conserves this property.
