Question

The flux limiter Ψ(r) of the second-order upwind scheme is __________

(a) r^2

(b) \(\frac{1}{2}r\)

(c) 2r

(d) r

The question was asked in an interview.

My doubt stems from Convection-Diffusion Problems topic in chapter Convection-Diffusion Problems of Computational Fluid Dynamics

Answer 1

The correct option is (d) r

Explanation: To find the flux limiter,

\(\phi_f=\phi_C+\frac{1}{2}\psi(r)(\phi_D-\phi_C)\)

For the second order upwind scheme,

\(\phi_f=\frac{3}{2}\phi_C-1\frac{1}{2}\phi_U\)

Equating both,

\(\frac{1}{2}\psi(r)(\phi_D-\phi_C)=\frac{3}{2}\phi_C-\phi_C-\frac{1}{2}\phi_U\)

\(\frac{1}{2}\psi(r)(\phi_D-\phi_C)=\frac{1}{2}(\phi_C-\phi_U)\)

\(\psi(r)=\frac{(\phi_C-\phi_U)}{(\phi_D-\phi_C)}=r\).