5. Partial Differential Equations

Finite Volume — Quiz

Test your understanding of finite volume with 5 practice questions.

Practice Questions

Question 1

What is the cell average $\bar u_i$ of a function $u(x)$ over the finite volume cell $[x_{i-1/2},x_{i+1/2}]$?

Question 2

A numerical flux function $F(u_L,u_R)$ in a finite volume scheme is called consistent with the physical flux $f(u)$ if it satisfies which property?

Question 3

According to Godunov’s theorem, what is the maximum order of accuracy that a linear monotone finite volume scheme can achieve?

Question 4

For the one-dimensional diffusion equation $u_t=D\,u_{xx}$ discretized with explicit Euler in time and central differences in space on a uniform grid, the stability condition on time step $\Delta t$ is:

Question 5

In finite volume methods for the linear advection equation $u_t+a\,u_x=0$, the Courant number $\nu$ is defined as: