diffusivity equation commonly used for pressure distribution prediction in porous media results from substituting equation of state and continuity equation in navier-stokes momentum equation. from mathematical point of view this equation format shows infinite propagation speed for pressure pulse through porous media, which is physically impossible. this issue may caused by numerous assumptions ...

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...

Abstract. This paper discusses the symbol of the Hessian of a shape optimization problem in a viscid, incompressible flow. The symbol of the Hessian for the Stokes shape optimization problem is analytically approximated by tracking a Fourier mode through the operators involved. We propose a discrete method for finding the symbol and confirm the correctness by comparison with the analytical data...

Multisummation provides a transparent description of Stokes matrices which is reviewed here together with some applications. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for a third Painlevé equation is made explicit. It is shown that the monodromy identity, relating the topological monodromy and Stokes matrices, is useful for some quantum differentia...

We present a finite element (FEM) simulation method for pore geometry fluid flow. Within the pore space, we solve the single-phase Reynold’s lubrication equation—a simplified form of the incompressible Navier–Stokes equation yielding the velocity field in a two-step solution approach. (1) Laplace’s equation is solved with homogeneous boundary conditions and a right-hand source term, (2) pore pr...

In this paper we study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature. We establish global well-posedness results with rough initial data.