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We consider a simple scalar reaction-advection-diffusion equation with ignition-type nonlinearity and discuss the following question: What kinds of velocity profiles are capable of quenching any given flame, provided the velocity's…
The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale "stone forests" of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan…
A nonlinear equation describing curved stationary flames with arbitrary gas expansion $\theta = \rho_{{\rm fuel}}/\rho_{{\rm burnt}}$, subject to the Landau-Darrieus instability, is obtained in a closed form without an assumption of weak…
We investigate the large-time dynamics of solutions of multi-dimensional reaction-diffusion equations with ignition type nonlinearities. We consider solutions which are in some sense locally persistent at large time and initial data which…
The motion of rarefied gases for uniform shear flow at the kinetic level is governed by the spatially homogeneous Boltzmann equation with a deformation force. In the paper we study the corresponding Cauchy problem with initial data of…
Theory of fast binary chemical reaction, ${\cal A}+{\cal B}\to{\cal C}$, in a statistically stationary chaotic flow at large Schmidt number ${Sc}$ and large Damk\"ohler number ${Da}$ is developed. For stoichiometric condition we identify…
Starting with an integral formulation of mass flow rate through an ensemble of isotherms constituting a statistically planar, turbulent premixed flame, a scaling for the corresponding turbulent flame speed is derived without invoking…
The present study addresses the reaction zone structure and burning mechanism of unstable detonations. Experiments investigated mainly two-dimensional methane-oxygen cellular detonations in a thin channel geometry. The sufficiently high…
The paper treats the propagation of a hydraulically driven crack. We explicitly write the local speed equation, which facilitates using the theory of propagating interfaces. It is shown that when neglecting the lag between the liquid front…
Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting…
This paper presents numerical and analytical investigation of gas flow in gas-dynamic filter - a device for cleaning gas from solid particles with counter flow of large water particles in order to prevent their release to the atmosphere.…
We study the nucleation and growth of flame fronts in slow combustion. This is modeled by a set of reaction-diffusion equations for the temperature field, coupled to a background of reactants and augmented by a term describing random…
In this paper, we have used the QUICK scheme of the finite volume method to investigate the problem of steady 2-D free convective incompressible flow with heat and mass transfer in an inclined rectangular domain at different Rayleigh…
Most mathematics and engineering textbooks describe the process of "subtracting off" the steady state of a linear parabolic partial differential equation as a technique for obtaining a boundary-value problem with homogeneous boundary…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…
A highly accurate method for simulating surfactant-covered droplets in two-dimensional Stokes flow with solid boundaries is presented. The method handles both periodic channel flows of arbitrary shape and stationary solid constrictions. A…
In the presence of a chemically active particle, a nearby chemically inert particle can respond to a concentration gradient and move by diffusiophoresis. The nature of the motion is studied for two cases: first, a fixed reactive sphere and…
We present a numerical method for the solution of interfacial growth governed by the Stefan model coupled with incompressible fluid flow. An algorithm is presented which takes special care to enforce sharp interfacial conditions on the…
A finite-volume method for the steady, compressible, reacting, turbulent Navier-Stokes equations is developed by using a steady-state preserving splitting scheme for the stiff source terms in chemical reaction. Laminar and turbulent…
A two-phase, low-Mach-number flow solver is created and verified for variable-density liquid and gas with phase change. The interface is sharply captured using a split Volume-of-Fluid method generalized for a non-divergence-free liquid…