2014/12/16 by Fereidoun Sabetghadam, Sabetghadam, Fereidoun
Engineering · #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Heat Transfer #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1412.5130
openalex publication_date 2014/12/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
The incompressible Navier-Stokes equations are re-formulated to involve an arbitrary time dilation; and in this manner, the modified Navier-Stokes equations are obtained which have some penalization terms in the right hand side. Then, the solid rigid bodies are modeled as the regions where time is dilated infinitely. The physical and mathematical properties of the modified equations and the penalization terms are investigated, and it is shown that the modified equations satisfy the no-slip, no-diffusion, no-advection, and no-pressure coupling conditions. The modified equations can be used in exact imposition of the solid rigid bodies on the incompressible Navier-Stokes equations. To show the capability of the modified equations, three classical exact solutions of the Navier-Stokes equations, that is, the Stokes first problem, the plane stagnation point flow, and the stokes flow over a sphere are re-solved exactly, this time in the presence of a solid region.