In the present work, the Roe, the Steger and Warming, the Van Leer, the Harten, the Frink, Parikh and Pirzadeh, the Liou and Steffen Jr. and the Radespiel and Kroll schemes are implemented, on a finite volume context and using an upwind and unstructured spatial discretization, to solve the Euler equations in the three-dimensional space. The Roe, the Harten, and the Frink, Parikh and Pirzadeh sc...

We study the generalized Forchheimer equations for slightly compressible fluids in porous media. The structural stability is established with respect to either the boundary data or the coefficients of the Forchheimer polynomials. An inhomogeneous Poincare-Sobolev inequality related to the non-linearity of the equation is used to study the asymptotic behavior of the solutions. Moreover, we prove...

where the symbols ∆, ∇, and ∇· stand for the Laplacian, gradient, and divergence operators, respectively (∆u is the vector of components ∆ui); the number μ is a viscous constant; f is a given vector function; β = (U,V)t is a given C1 function. The system (1.1) may be obtained by linearizing the steady-state barotropic compressible viscous Navier-Stokes equations without an ambient flow (see [8,...

In this work, we propose a new way of splitting the flux function of the isentropic compressible Euler equations at low Mach number into stiff and non-stiff parts. Following the IMEX methodology, the latter ones are treated explicitly, while the first ones are treated implicitly. The splitting is based on the incompressible limit solution, which we call reference solution (RS). An analysis conc...

Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...

The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows, including nearly incompressible low Mach number flows, flows with strong shocks, multicomponent flows with high density ratios and interfacial physics, inviscid and viscous flows, as well as flows featuring combinations of these phenomena and various interaction...

The aim of this paper is to develop a mathematical model to simulate mosquito dispersal and its control taking into account environmental parameters, like wind, temperature, or landscape elements. We particularly focus on Aedes albopictus mosquito which is now recognized as a major vector of human arboviruses, like chikungunya, dengue, or yellow fever. One way to prevent those epidemics is to c...

Kinetic schemes for compressible flow of gases are constructed by exploiting the connection between Boltzmann equation and the Navier-Stokes equations. This connection allows us to construct a flux splitting for the NavierStokes equations based on the direction of molecular motion from which a numerical flux can be obtained. The naive use of such a numerical flux function in a discontinuous Gal...

An exact form is presented for the axial-vector Bethe-Salpeter equation, which is valid when the quark-gluon vertex is fully dressed. A Ward-Takahashi identity for the Bethe-Salpeter kernel is derived therefrom and solved for a class of dressed quark-gluon-vertex models. The solution provides a symmetry-preserving closed system of gap and vertex equations. The analysis can be extended to the ve...

Numerical simulations of a spacecraft at reentry conditions are presented. The fluid at such conditions is modeled as a reacting gas in thermal and chemical nonequilibrium. The reacting gas is modeled using a standard finite rate chemistry model for air. A twotemperature model is used to account for the thermal nonequilibrium effects. The finitevolume method is used to solve the set of differen...