The hydrodynamical model of quantum mechanics based on the Schrödinger equation is combined with the magnetohydrodynamical term to form so called quantum magnetohydrodynamic equation. It is shown that the quantum correction to the Alfvén waves follows from this new equation. The possible generalization is considered for the so called nonlinear Schrödinger equation and for the situation where di...

The Burgers’ equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank – Nicholson, used for solving the one-dimensional Burgers’ equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to...

to perhaps the fact that the turbulence model equations are solved only to obtain the eddy viscosity and also the Many researchers use a time-lagged or loosely coupled approach in solving the Navier–Stokes equations and two-equation turbuconvenience of simply adding separate routines to an exlence model equations in a time-marching method. The Navier– isting Navier–Stokes code. Consequently, ma...

We demonstrate that the Navier-Stokes equation can be covariantized under the full infinite dimensional Galilean Conformal Algebra (GCA), such that it reduces to the usual Navier-Stokes equation in an inertial frame. The covariantization is possible only for incompressible flows, i.e. when the divergence of the velocity field vanishes. Using the continuity equation, we can fix the transformatio...

This note details the derivation of the generalized advective-diffusive equation system for the 2D space-time incompressible Navier-Stokes governing equations, in conservation form.