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Which of these time-steps are used to approximate the value at time-step t-\(\frac{\Delta t}{2}\) using the Crank-Nicolson scheme for finite volume approach?(a) t and t+Δ t(b) t and t-Δ t(c) t and t-\(\frac{\Delta t}{2}\)(d) t and t+\(\frac{\Delta t}{2}\)The question was asked during a job interview.My doubt is from Transient Flows in portion Transient Flows of Computational Fluid Dynamics |
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Answer» RIGHT option is (b) t and t-Δ t The BEST I can explain: The Crank-Nicolson scheme USES the cell centres of both the cells which share the face which is considered. The face considered here is t-\(\frac{\Delta t}{2}\) . It is SHARED by the faces t and t-Δ t. So, the scheme uses both of these values for the approximation. |
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