General and exact pressure evolution equation

On exactly incompressible DG FEM pressure splitting schemes for the Navier-Stokes equation

We compare three iterative pressure correction schemes for solving the Navier-Stokes equations with a focus on exactly divergence free solution with higher order discontinuous Galerkin discretisations. The investigated schemes are the incremental pressure correction scheme on the standard differential form (IPCS-D), the same scheme on algebraic form (IPCS-A), and the semi-implicit method for pressure linked equations (SIMPLE). We show algebraically and through numerical examples that the IPCS-A and SIMPLE schemes are exactly mass conserving due to the algebraic pressure correction, while the I…

An exact pressure evolution equation for the incompressible Navier-Stokes equations

In this paper the issue of the determination of the fluid pressure in incompressible fluids is addressed, with particular reference to the search of algorithms which permit to advance in time the fluid pressure without actually solving numerically the Poisson equation. Based on an inverse kinetic approach recently proposed for the incompressible Navier-Stokes equations we intend to prove that an exact evolution equation can be obtained which advances in time self-consistently the fluid pressure. The new equation is susceptible of numerical implementation in Lagrangian CFD simulation codes.

Simulating temporal evolution of pressure in two-phase flow in porous media

We have simulated the temporal evolution of pressure due to capillary and viscous forces in two-phase drainage in porous media. We analyze our result in light of macroscopic flow equations for two-phase flow. We also investigate the effect of the trapped clusters on the pressure evolution and on the effective permeability of the system. We find that the capillary forces play an important role during the displacements for both fast and slow injection rates and both when the invading fluid is more or less viscous than the defending fluid. The simulations are based on a network simulator modeling…

非等温全局压力精确性在具有演化的裂缝孔隙率多相流中

Nonisothermal global-pressure exactness in fractured multiphase flow with aperture feedback

本文研究了非等温条件下多相流中全局压力公式的精确性条件，推导了温度依赖的渗流和毛细压的精确性标准，并通过数值实验验证了不同精确性区域的转变。

Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: toward linking energy cascade and instabilities

We derive a first exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to…

Exact pressure evolution equation for incompressible fluids

An important aspect of computational fluid dynamics is related to the determination of the fluid pressure in isothermal incompressible fluids. In particular this concerns the construction of an exact evolution equation for the fluid pressure which replaces the Poisson equation and yields an algorithm which is a Poisson solver, i.e., it permits to time-advance exactly the same fluid pressure \textit{without solving the Poisson equation}% . In fact, the incompressible Navier-Stokes equations represent a mixture of hyperbolic and elliptic pde's, which are extremely hard to study both analytically…