Question

Consider the one-dimensional heat conduction equation. Apply forward difference method to approximate time rate and central difference method to approximate x-derivative. The resulting equation is in _____________

(a) Implicit linear form

(b) Explicit linear form

(c) Explicit non-linear form

(d) Implicit non-linear form

The question was asked in a job interview.

I need to ask this question from Explicit and Implicit Finite Difference Methods topic in section Finite Difference Methods of Computational Fluid Dynamics

Answer 1

Correct answer is (b) Explicit linear form

Best explanation: The one-dimensional heat conduction equation is

\(\frac{\partial T}{\partial t}=α \frac{\partial^2 T}{\partial t^2} \)

Applying the difference approximations,

\(\frac{T_i^{n+1}-T_i^n}{\Delta t}=\alpha \frac{T_{i+1}^n-2T_i^n+T_{i-1}^n}{(\Delta x^2)} \)

\(T_i^{n+1}=T_i^n+\alpha\frac{\Delta t(T_{i+1}^n-2T_i^n+T_{i-1}^n)}{(\Delta x^2)} \)

The equation is in explicit linear form.