Exact solution of the diffusionconvection equation Convection-diffusionequationinradialco-ordinates:CV0tr CrD2rC21rCr Boundaryconditions:C(r0,t)C0(finite)C(rL,t)0 Initialconditions:C(r,t0)f(r)NS,LPPD 3 Generalsolution,Separationofvariables.Cr,tRrTt Substitutingthisintheconvection-diffusionequation.D...
1, the species transport occurs due to diffusion, with diffusion coefficient D, and convection, due to the velocity vector V, of the bulk fluid flow partial deriv C/partial deriv t + V(r)▽C = ▽(D▽C) (1)Solution of this equation is invaluable for validating the accuracy of ...
《传热与流体流动的数值计算》学习草记 5 Convection and Diffusion 5.1 The Task 5.2 Steady One-dimensional Convection and Diffusion 5.2.1 A Preliminary Derivation 5.2.2 The Upwind Scheme 5.2.3 The Exact Solution 5.2.4 The Exponential Scheme 5.2.5 The Hybrid Scheme 5.2.6 The Power-Law Scheme 5.2...
This sequencing method allows us to solve both hyperbolic and parabolic equations and to extend the frequency response of the numerical solution. Simulation results are given for linear and nonlinear reaction kinetics. These are compared with the exact solution for the high diffusion case and with ...
In this study we derive a mathematically rigorous kernel function, which accounts for the interaction among particles, within the framework of the particle method, to predict a computationally more accurate solution for the convection-diffusion equation investigated at low as well as high Peclet ...
The unsteady convection-diffusion equation with constant coefficients admits an exact solution in the form of a convolution integral, which provides an exp... MORTON K. W.,SOBEY I. J. - 《Ima Journal of Numerical Analysis》 被引量: 27发表: 1993年 High-Order Compact Difference Scheme for Co...
Yee, E., 1993, Application of the decomposition method to the solution of the reaction-convection-diffusion equation. Applied Mathematics and Computation, 56, 1-27.YEE E. Application of the decomposition method to the solution of the reaction convection-diffusion equation[J].Applied Mathematics and...
where vapor pressurepvscan be expressed through density (vapor concentration)ρvsin accordance with Mendeleev-Clapeyron equation, since the vapor-air mixture under the atmospheric pressure is considered the ideal gas (coefficientDis the diffusion coefficient for gas-vapor mixture, parameterBMis the Spalding...
method from a physical viewpoint and proved that the Petrov-Galerkin methods can be optimal in the sense of adding an exact amount of diffusion so as to balance the artificial diffusion and obtain the exact solution at nodes when a uniform mesh is used and the equation has constant ...
Convection-diffusion reactions are used in many applications in science and engineering. In many of the applications, the governing equations are non-linear and this leads to difficulties in obtaining exact or analytical solutions. Under the circumstances where solutions are needed, the need for numeri...