How is the value \((\frac{\partial \rho}{\partial t})_{i,j}^{av}\) obtained in the MacCormack’s expansion to find \(\rho_{i,j}^{t+\Delta t}\)?(a) Truncated mean of \((\frac{\partial\rho}{\partial t})_{i,j}^t and (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)(b) Weighted average of \((\frac{\partial\rho}{\partial t})_{i,j}^t and (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)(c) Geometric mean of \((\frac{\partial\rho}{\partial t})_{i,j}^t and (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)(d) Arithmetic mean of \((\frac{\partial\rho}{\partial t})_{i,j}^t and (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)I had been asked this question during an interview.I need to ask this question from Finite Difference Methods topic in division Finite Difference Methods of Computational Fluid Dynamics

How is the value \((\frac{\partial \rho}{\partial t})_{i,j}^{av}\) obt

1.	How is the value \((\frac{\partial \rho}{\partial t})_{i,j}^{av}\) obtained in the MacCormack’s expansion to find \(\rho_{i,j}^{t+\Delta t}\)?(a) Truncated mean of \((\frac{\partial\rho}{\partial t})_{i,j}^t and (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)(b) Weighted average of \((\frac{\partial\rho}{\partial t})_{i,j}^t and (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)(c) Geometric mean of \((\frac{\partial\rho}{\partial t})_{i,j}^t and (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)(d) Arithmetic mean of \((\frac{\partial\rho}{\partial t})_{i,j}^t and (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\)I had been asked this question during an interview.I need to ask this question from Finite Difference Methods topic in division Finite Difference Methods of Computational Fluid Dynamics
Answer» Correct CHOICE is (d) ARITHMETIC MEAN of \((\frac{\partial\rho}{\partial t})_{i,j}^t and (\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}\) Explanation: The VALUE of \((\frac{\partial \rho}{\partial t})_{i,j}^{av}\) is the arithmetic mean of \((\frac{\partial \rho}{\partial t})_{i,j}\) at t and \((\frac{\partial \rho}{\partial t})_{i,j}\) at t+Δt. \((\frac{\partial \rho}{\partial t})_{i,j}^{av}=\frac{1}{2}[(\frac{\partial\rho}{\partial t})_{i,j}^t+(\frac{\partial\rho}{\partial t})_{i,j}^{t+\Delta t}]\).

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