This paper focuses on the notion of suitable weak solutions for the three-dimensional incompressible Navier–Stokes equations and discusses the relevance of this notion to Computational Fluid Dynamics. The purpose of the paper is twofold (i) to recall basic mathematical properties of the three-dimensional incompressible Navier-Stokes equations and to show how they relate to LES (ii) to introduce...

In this paper a new set of Boussinesq wave equations with improved linear dispersion properties is proposed for extending its application to deeper water without having its mathematical form changed. The improvements are due to the combination of a generalized set of Boussinesq wave equations expressed in terms of any velocity, with additional dispersive terms obtained by invoking the linear sh...

Abstract. A Boussinesq model for the Bénard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier-Stokes equations and the transport equation for temperature. Large deviations are proved, using a weak convergence approach based on a variational representation of functionals of infinite dimensional...

Application of the computer simulation for solving the incompressible flow problems motivates developing efficient and accurate numerical models. The set of Inviscid Incompressible Euler equations can be applied for wide range of engineering applications. For the steady state problems, the equation of continuity can be simultaneously solved with the equations of motion in a coupled manner using...

The semi-geostrophic equations are used in meteorology. They appear as a variant of the two-dimensional Euler incompressible equations in vorticity form, where the Poisson equation that relates the stream function and the vorticity field is just replaced by the fully non linear elliptic Monge-Ampère equation. This work gathers new results concerning the semi-geostrophic equations: Existence and...

The paper presents analysis of two-dimensional non-Newtonian incompressible viscous flow between parallel plates. The governing problem of momentum equations are reduced to NODE using similarity transformations. The resulting equation is solved using series solution and homotopy analysis method. These methods have advantages over pure numerical methods for obtaining the derived quantities accur...

Most models of astrophysical flows employ a ``sound-proof'' approximation, such as the Boussinesq, anelastic, and pseudo-incompressible models, which remove acoustic waves from governing equations. Here, we address accuracy each these for describing magnetic buoyancy in solar interior. We introduce general sound-proof model compare its behavior to that fully compressible system within range ast...

Abstract Macrosegregation presents a considerable defect in the continuous casting of billets and can critically affect final properties product. The numerical modelling help to predict better understand segregation flow patterns inside mould. process is modelled with physical model described by set conservation equations describing t heat transfer, turbulence, fluid flow, solidification segreg...

The Boussinesq equation is a mathematics model of thermohydraulics, which consists of equations of fluid and temperature in the Boussinesq approximation.The deterministic case has been studied systematically by many authors (e.g., see [1– 3]). However, in many practical circumstances, small irregularity has to be taken into account.Thus, it is necessary to add to the equation a random force, wh...