共查询到20条相似文献,搜索用时 31 毫秒
1.
Science China Mathematics - We consider the full compressible Navier-Stokes equations with reaction diffusion. A global existence and uniqueness result of the strong solution is established for the... 相似文献
2.
A two-dimensional model for the diffusion and chemical interactionin a uniform flow of two adjacent pollutant discharge plumes,assumed to react to form a nonpollutant product, is studied.Analysis involving Hermite polynomials is used to derive, undera near-Gaussian approximation, a system of ordinary differentialequations. Numerical solutions of these equations are displayedfor various initial conditions. It is found that the qualitativebehaviour of the drift, spread, and total amount of each pollutantfar downstream depends significantly on how closely the dischargerates are chemically matched, and also on whether the two dischargesare coincident, side-by-side, or one upstream of the other.Results arc also compared with a full numerical solution ofthe model equations. An appendix contains a study of the casein which the discharge rates are exactly matched. 相似文献
3.
Jürgen Geiser 《Numerical Methods for Partial Differential Equations》2012,28(4):1252-1282
The motivation is driven by deposition processes based on chemical vapor problems. The underlying model problem is based on coupled transport–reaction equations with mobile and immobile areas. We deal with systems of ordinary and partial differential equations. Such equation systems are delicate to solve and we introduce a novel solver method, that takes into account ways to solve analytically parts of the transport and reaction equations. The main idea is to embed the analytical and semianalytical solutions, which can then be explicitly given to standard numerical schemes of higher order. The numerical scheme is based on flux‐based characteristic methods, which is a finite volume method. Such a method is an attractive alternative to the standard numerical schemes, which fully discretize the full equations. We instead reduce the computational time while embedding fast computable analytical parts. Here, we can accelerate the solver process, with a priori explicitly given solutions. We will focus on the derivation of the analytical solutions for general and special solutions of the characteristic methods that are embedded into a finite volume method. In the numerical examples, we illustrate the higher‐order method for different benchmark problems. Finally, the method is verified with realistic results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012 相似文献
4.
Matthias Wiedmer. 《Mathematics of Computation》2000,69(229):83-101
We consider the equations of stationary incompressible magnetohydrodynamics posed in three dimensions, and treat the full coupled system of equations with inhomogeneous boundary conditions. We prove the existence of solutions without any conditions on the data. Also we discuss a finite element discretization and prove the existence of a discrete solution, again without any conditions on the data. Finally, we derive error estimates for the nonlinear case.
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The Ritz-Galerkin solution of a linear integral or differentialequation or set of equations leads to a set of linear algebraicequations, the structure of which depends on the type of expansionset used. For a finite-element expansion, the matrix involvedis sparse, and reasonably efficient solution techniques areknown. We study here the alternative case when a "global" expansionis chosen. Then the matrix involved is in general full, buthas nonetheless a characteristic structure; we discuss the waysin which this structure can be used to yield efficient solutionmethods. Our main result is that a block iterative method canyield an arbitrarily high convergence rate; however, we alsoconsider the stability of a direct solution of the equations. 相似文献
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A generic averaging theorem is proven for systems of ODEs with two-time scales that cannot be globally transformed into the usual action-angle variable normal form for such systems. This theorem is shown to apply to certain Fourier-space truncations of the non-isentropic slightly compressible Euler equations of fluid mechanics. For the full Euler equations, we derive formally the generic limit equations and analyze some of their properties. In the one-dimensional case, we prove a generic converic convergence result for the full Euler equations, analogous to the result for ODEs. By making use of special properties of the one-dimensional equations, we prove convergence to the solution of a more complicated set of averaged equations when the genericity assumptions fail. 相似文献
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Gleiciane da Silva Aragão Sergio Muniz Oliva 《Journal of Differential Equations》2012,253(9):2573-2592
In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction–diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter ? goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. 相似文献
8.
《Journal of Computational and Applied Mathematics》2002,145(2):493-503
We consider an initial value problem for the second-order differential equation with a Dirichlet-to-Neumann operator coefficient. For the numerical solution we carry out semi-discretization by the Laguerre transformation with respect to the time variable. Then an infinite system of the stationary operator equations is obtained. By potential theory, the operator equations are reduced to boundary integral equations of the second kind with logarithmic or hypersingular kernels. The full discretization is realized by Nyström's method which is based on the trigonometric quadrature rules. Numerical tests confirm the ability of the method to solve these types of nonstationary problems. 相似文献
9.
Andrei Korobeinikov John Norbury Graeme C. Wake 《Nonlinear Analysis: Real World Applications》2009,10(1):93-103
Spatial distribution of interacting chemical or biological species is usually described by a system of reaction–diffusion equations. In this work we consider a system of two reaction–diffusion equations with spatially varying diffusion coefficients which are different for different species and with forcing terms which are the gradient of a spatially varying potential. Such a system describes two competing biological species. We are interested in the possibility of long-term coexistence of the species in a bounded domain. Such long-term coexistence may be associated either with a periodic in time solution (usually associated with a Hopf bifurcation), or with time-independent solutions. We prove that no periodic solution exists for the system. We also consider some steady states (the time-independent solutions) and examine their stability and bifurcations. 相似文献
10.
We consider a model equations describing the coagulation process of a gas on a surface. The problem is modeled by two coupled equations. The first one is a nonlinear transport equation with bilinear coagulation operator while the second one is a nonlinear ordinary differential equation. The velocity and the boundary condition of the transport equation depend on the supersaturation function satisfying the nonlinear ode. We first prove global existence and uniqueness of solution to the nonlinear transport equation then, we consider the coupled problem and prove existence in the large of solutions to the full coagulation system. 相似文献
11.
Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws 总被引:3,自引:0,他引:3
Yuxi Zheng 《应用数学学报(英文版)》2006,22(2):177-210
We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach's experiment for the compressible Euler system, i.e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations. 相似文献
12.
Abdelhadi Es-Sarhir Michael Scheutzow Jonas M. Tölle Onno van Gaans 《Applied Mathematics and Optimization》2013,68(2):275-287
We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller property of the solution to show existence of an invariant measure. As an application we discuss stochastic reaction diffusion equations. 相似文献
13.
In this paper, we focus on maximum principles of a time–space fractional diffusion equation. Maximum principles for classical solution and weak solution are all obtained by using properties of the time fractional derivative operator and the fractional Laplace operator. We deduce maximum principles for a full fractional diffusion equation, other than time-fractional and spatial-integer order diffusion equations. 相似文献
14.
We present a method for the solution of transient flow in a multi-port fluid device with arbitrary geometry. The method is applicable to fluid devices where the fluid motion is primarily inviscid throughout the volume, but locally near a device port some accommodation to viscous flow is introduced. The internal flow is characterized by an array of purely geometrical factors between ports, essentially a set of generalized impedances; the state variables elicited are the average volume flow rates through the device ports. The method creates a set of coupled non-linear time-dependent ordinary differential equations. The solution to this set of equations is much faster, typically by orders of magnitude, than a single run of a transient CFD model. We demonstrate our method with a simple example; we show that the results of the method agree well with a full CFD calculation. 相似文献
15.
Tatsuo Iguchi 《偏微分方程通讯》2013,38(1):37-85
The Korteweg–de Vries (KdV) equation is known as a model of long waves in an infinitely long canal over a flat bottom and approximates the 2-dimensional water wave problem, which is a free boundary problem for the incompressible Euler equation with the irrotational condition. In this article, we consider the validity of this approximation in the case of the presence of the surface tension. Moreover, we consider the case where the bottom is not flat and study an effect of the bottom to the long wave approximation. We derive a system of coupled KdV like equations and prove that the dynamics of the full problem can be described approximately by the solution of the coupled equations for a long time interval. We also prove that if the initial data and the bottom decay at infinity in a suitable sense, then the KdV equation takes the place of the coupled equations. 相似文献
16.
Ju Hong Kim 《Journal of Applied Mathematics and Computing》2002,9(2):373-389
In this paper we formulate the linear theory for compressible fluids in cylindrical geometry with small perturbation at the material interface. We derive the first order equations in the smooth regions, boundary conditions at the shock fronts and the contact interface by linearizing the Euler equations and Rankine-Hugoniot conditions. The small amplitude solution formulated in this paper will be important for calibration of results from full numerical simulation of compressible fluids in cylindrical geometry. 相似文献
17.
We investigate the properties of dissipative full discretizations for the equations of motion associated with models of flow and radiative transport inside stars. We derive dissipative space discretizations and demonstrate that together with specially adapted total-variation-diminishing (TVD) or strongly stable Runge-Kutta time discretizations with adaptive step-size control this yields reliable and efficient integrators for the underlying high-dimensional nonlinear evolution equations. For the most general problem class, fully implicit SDIRK methods are demonstrated to be competitive when compared to popular explicit Runge-Kutta schemes as the additional effort for the solution of the associated nonlinear equations is compensated by the larger step-sizes admissible for strong stability and dissipativity. For the parameter regime associated with semiconvection we can use partitioned IMEX Runge-Kutta schemes, where the solution of the implicit part can be reduced to the solution of an elliptic problem. This yields a significant gain in performance as compared to either fully implicit or explicit time integrators. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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In this article, we use the decay character of initial data to compare the energy decay rates of solutions to different compressible approximations to the Navier- Stokes equations.We show that the system having a nonlinear damping term has slower decay than its counterpart with an advection-like term. Moreover, me characterize a set of initial data for which the decay of the first system is driven by the difference between the full solution and the solution to the linear part, while for the second system the linear part provides the decay rate. 相似文献
20.
S. Meliani & G. Panasenko 《Applicable analysis》2013,92(3):229-245
We consider a composite material composed of carbon or glass fibres included in a resin which becomes solid when it is heated up (the reaction of reticulation). A mathematical model of the cure process is given by a kinetic equation describing the evolution of the reaction of reticulation coupled with the heat equation. The geometry of the composite material is periodic, with a small period ? >0, thus we get a coupled system of nonlinear partial differential equations. First we prove the existence and uniqueness of a solution by using a fixed point theorem and we obtain a priori estimates. Then we derive the homogenized problem which describes the macroscopic behaviour of the material. We prove the convergence of the solution of the problem to the solution of the homogenized problem when ? tends to zero as well as the estimates for the difference of the exact and the approximate solutions. 相似文献