Flux Splitting for stiff equations: A notion on stability

For low Mach number flows, there is a strong recent interest in the development and analysis of IMEX (implicit/explicit) schemes, which rely on a splitting of the convective flux into stiff and nonstiff parts. A key ingredient of the analysis is the so-called Asymptotic Preserving (AP) property, which guarantees uniform consistency and stability as the Mach number goes to zero. While many authors have focussed on asymptotic consistency, we study asymptotic stability in this paper: does an IMEX scheme allow for a CFL number which is independent of the Mach number? We derive a stability criterion for a general linear hyperbolic system. In the decisive eigenvalue analysis, the advective term, the upwind diffusion and a quadratic term stemming from the truncation in time all interact in a subtle way. As an application, we show that a new class of splittings based on characteristic decomposition, for which the commutator vanishes, avoids the deterioration of the time step which has sometimes been observed in the literature

A note on adjoint error estimation for one-dimensional stationary balance laws with shocks

We consider one-dimensional steady-state balance laws with discontinuous solutions. Giles and Pierce realized that a shock leads to a new term in the adjoint error representation for target functionals.This term disappears if and only if the adjoint solution satisfies an internal boundary condition. Curiously, most computer codes implementing adjoint error estimation ignore the new term in the functional, as well as the internal adjoint boundary condition. The purpose of this note is to justify this omission as follows: if one represents the exact forward and adjoint solutions as vanishing viscosity limits of the corresponding viscous problems, then the internal boundary condition is naturally satisfied in the limit

Инвестиционная привлекательность предприятий-резидентов особых экономических зон на примере Томской области

В статье обобщаются и выявляются возможности повышения инвестиционной привлекательности предприятий при вхождении в особую экономическую зону (ОЭЗ), на основе опроса исследуется отношение иностранных партнеров к привлекательности резидентов ОЭЗ для инвестиций и долгосрочного сотрудничества, анализируются изменения результатов работы компаний после вхождения в ОЭЗ на примете ОЭЗ Томской области