In most combustion devices, the Mach number is small, and the most efficient computational approach is the solving of the low-Mach number formulation of the Navier-Stokes equations. In this approach, the acoustic waves propagate at an infinite speed. Nevertheless, when the acoustic speed plays an important role, as in the formation of instabilities, the compressible Navier-Stokes equations must...

SUMMARY An asymptotic analysis of the compressible Euler equations in the limit of vanishing Mach numbers is used as a guideline for the development of a low Mach number extension of an explicit higher order shock capturing scheme. For moderate and large Mach numbers the underlying explicit compressible ow solver is active without modiication. For low Mach numbers, the scheme employs an operato...

Fey’s Method of Transport (MoT ) is a multidimensional flux-vector-splitting scheme for systems of conservation laws. Similarly to its one-dimensional forerunner, the Steger–Warming scheme, and several other upwind finite-difference schemes, the MoT suffers from an inconsistency at sonic points when used with piecewise-constant reconstructions. This inconsistency is due to a cell-centered evolu...

We analyze the conservation properties of various discretizations system compressible Euler equations for shock-free flows, with special focus on treatment energy equation and induced discrete other thermodynamic quantities. The analysis is conducted both theoretically numerically considers two important factors characterizing formulations, namely choice splitting used in discretization convect...

We prove that the smooth solutions to the Cauchy problem for the three-dimensional compressible barotropic magnetohydrodynamic equations with conserved total mass and finite total energy lose the initial smoothness within a finite time. Further, we show that the same result holds for the solution to the Cauchy problem for the multidimensional compressible NavierStokes system. Moreover, for the ...

Because of the global warming and the rising sea level, residents living in southwestern coastland, Taiwan are faced with the submerged land and may move to higher elevation area. It is desirable to discuss the key consideration factor for selecting the migration location under five dimensions of security”, “health”, “convenience”, “comfort” and “socio-economic” based on the document reviews. T...

Let A be an n × n subgaussian matrix (entries are i.i.d. subgaussian r.v’s with variance 1). There are two reasons for the invertibility of A, depending on the nature of the unit vector on which A is acting – either compressible or incompressible. We recall that compressible vectors are those whose distance is at most some constant ρ from the set of (δn)-sparse vectors, and incompressible vecto...

The simplifications required to apply the Boussinesq approximation to compressible flow are compared with those in an incompressible fluid. The larger degree of approximation required to describe mass conservation in a stratified compressible fluid with the Boussinesq continuity equation has led to the development of several different sets of “anelastic” equations that may be regarded as genera...

Stratospheric sudden warmings are the clearest and strongest manifestation of dynamical coupling in the stratosphere–troposphere system. While many sudden warmings have been individually documented in the literature, this study aims at constructing a comprehensive climatology: all major midwinter warming events are identified and classified, in both the NCEP–NCAR and 40-yr ECMWF Re-Analysis (ER...