Question

How is the value ((frac{partial ho}{partial t})_{i,j}^{av}) obtained in the MacCormack’s expansion to find ( ho_{i,j}^{t+Delta t})?

(a) Truncated mean of ((frac{partial ho}{partial t})_{i,j}^t and (frac{partial ho}{partial t})_{i,j}^{t+Delta t})

(b) Weighted average of ((frac{partial ho}{partial t})_{i,j}^t and (frac{partial ho}{partial t})_{i,j}^{t+Delta t})

(c) Geometric mean of ((frac{partial ho}{partial t})_{i,j}^t and (frac{partial ho}{partial t})_{i,j}^{t+Delta t})

(d) Arithmetic mean of ((frac{partial ho}{partial t})_{i,j}^t and (frac{partial ho}{partial t})_{i,j}^{t+Delta t})

Answer 1

Correct choice is (d) Arithmetic mean of ((frac{partial ho}{partial t})_{i,j}^t and (frac{partial ho}{partial t})_{i,j}^{t+Delta t})

Explanation: The value of ((frac{partial ho}{partial t})_{i,j}^{av}) is the arithmetic mean of ((frac{partial ho}{partial t})_{i,j}) at t and ((frac{partial ho}{partial t})_{i,j}) at t+Δt.

((frac{partial ho}{partial t})_{i,j}^{av}=frac{1}{2}[(frac{partial ho}{partial t})_{i,j}^t+(frac{partial ho}{partial t})_{i,j}^{t+Delta t}]).