A method of fluid dynamic analysis based on Navier-Stokes equation and conservation equation on fluid mechanical energy

When people solved the Navier-Stokes equation to find fluid velocity and pressure, they usually use the SIMPLE algorithm developed by Patankar and Spalding. Due to lack of independent partial differential equation for the pressure, the Navier-Stokes equation is solved numerically by pressure correction and iteration methods. In this paper, however, based on constructing a constitutive relation between fluid power flux and pressure gradient, a conservation equation on fluid mechanical energy was established. Thus, the Navier-Stokes equation can be solved by directly coupling the proposed conservation equation to find velocity and pressure in the flow field.