To prevent epidemics of mosquito-transmitted diseases like Chikungunya in Réunion Island, we develop tools to control its principal vector, Aedes albopictus. Biological control tools, like the Sterile Insect Technique (SIT), are of great interest as an alternative to chemical control tools which are very detrimental to environment. The success of SIT is based on a good knowledge of the biology ...

We establish a rate of convergence for a semi-discrete operator splitting method applied to Hamilton-Jacobi equations with source terms. The method is based on sequentially solving a Hamilton-Jacobi equation and an ordinary diierential equation. The Hamilton-Jacobi equation is solved exactly while the ordinary diierential equation is solved exactly or by an explicit Euler method. We prove that ...

The development of flux-vector splitting through the 1970s and 1980s is reviewed. Attention is given to the diffusive nature of flux-vector splitting, which makes it an undesirable technique for approximating the inviscid fluxes in a Navier-Stokes solver. Several proposed improvements, including a brandnew one, are discussed and illustrated by a simple, yet revealing, numerical test case. Final...

The Dirac particle, i.e. the dynamic system SD, described by the free Dirac equation is investigated. Although the Dirac equation is written usually in the relativistically covariant form, the dynamic system SD is not completely relativistic, because its description contains such absolute objects as γ-matrices γk, forming a matrix vector. By means of the proper change of variables the γ-matrice...

The Dirac particle, i.e. the dynamic system SD, described by the free Dirac equation is investigated. Although the Dirac equation is written usually in the relativistically covariant form, the dynamic system SD is not completely relativistic, because its description contains such absolute objects as γ-matrices γk, forming a matrix vector. By means of the proper change of variables the γ-matrice...

This article presents a time-accurate numerical method using high-order accurate compact finite difference scheme for the incompressible Navier–Stokes equations. The method relies on the artificial compressibility formulation, which endows the governing equations a hyperbolic–parabolic nature. The convective terms are discretized with a third-order upwind compact scheme based on flux-difference...

As a continuous eeort to understand the Godunov-type schemes, following the paper \Projection in this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers. More speciically, the underlying dynamics of Flux Vector Splitting (FVS) and Flux Diierence Splitting (FDS) schemes will be analyzed. Since the FVS scheme and the Kinetic Flux Vector Splitting (...

Numerical simulations of axisymmetric flows over reentry configurations at hypersonic conditions using a Navier-Stokes solver are presented. The Navier-Stokes equations are modified using Park’s two-temperature model to account for thermochemical nonequilibrium and weak ionization effects. The finite-volume method is used to solve the set of differential equations. The code has the capability t...

Numerical simulations of axisymmetric flows over the FIRE-II spacecraft at reentry conditions using a Navier-Stokes solver being developed at the University of Michigan are presented. The finite-volume method is used to solve the set of differential equations. The code has the capability to handle any mix of hexahedra, tetrahedra, prisms and pyramids in 3D or triangles and quadrilaterals in 2D....

Given a bounded autonomous vector field b : R2 → R2, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation ∂tu + b · ∇u = 0. Assuming that b is of class BV and it is nearly incompressible, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [10] (wh...