Question

Which of these values used to find \((\frac{\partial \rho}{\partial t})_{i,j}^{av}\) is a predicted one?

(a) \((\frac{\partial\rho}{\partial t})_{i,j}^t\)

(b) Neither \((\frac{\partial\rho}{\partial t})_{i,j}^t nor (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)

(c) \((\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)

(d) Both \((\frac{\partial\rho}{\partial t})_{i,j}^t and (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)

I had been asked this question at a job interview.

My enquiry is from Finite Difference Methods in division Finite Difference Methods of Computational Fluid Dynamics

Answer 1

Right answer is (c) \((\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)

Easiest explanation: \((\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\) is predicted using the continuity equation and the value of \(\rho_{i,j}^{t+\Delta t}\) in the process of finding \((\frac{\partial \rho}{\partial t})_{i,j}^{av}\). The continuity equation is used as we need the time rate of change of density.