Contents
What is the difference between convection and diffusion?
Diffusion occurs via the random motion of molecules; movement is from high to low concentration and depends upon the size of the molecule. Convection is the transport of a substance by bulk flow, where bulk flow is often the movement of fluid down a pressure gradient.
What is the main advantage in implicit methods?
The principal reason for using implicit solution methods, which are more complex to program and require more computational effort in each solution step, is to allow for large time-step sizes. A simple qualitative model will help to illustrate how this works.
How to integrate a diffusion model forward in time?
We want to integrate the model forward in time to model the changes in the field u ( x). 2. Discretizing the diffusion operator in space ¶ Solving a differential equation on a computer always requires some approximation to represent the continuous function u ( x, t) and its derivatives in terms of discrete quantities (arrays of numbers).
Are there finite difference schemes for heat transfer?
Abstract: This article deals with finite- difference schemes of two-dimensional heat transfer equations with moving boundary. The method is suggested by solving sample problem in two-dimensional solidification of square prism. The finite-difference scheme improved for this goal is based on the Douglas equation.
Is the FTCS scheme for diffusion equations stable?
We conclude the the FTCS scheme is stable so long as this stability condition is met: The maximum timestep we can use with the FTCS scheme for the diffusion equation is proportional to Δ x 2. A doubling of the spatial resolution would require a 4x shorter timestep to preserve numerical stability.
How to discretize the diffusion operator in space?
Discretizing the diffusion operator in space ¶ Solving a differential equation on a computer always requires some approximation to represent the continuous function u ( x, t) and its derivatives in terms of discrete quantities (arrays of numbers). We have already dealt with simple discretization of the time derivative back in Lecture 2.