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InterviewSolution
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The extra term added while discretizing the transient term of a flow with density ρ and flow variable φ using the first-order explicit Euler scheme is _________(a) \(\Delta t\frac{\partial^2(\rho\phi)}{\partial t^2}\)(b) \(-\Delta t\frac{\partial^2(\rho\phi)}{\partial t^2}\)(c) \(\frac{\Delta t}{2}\frac{\partial^2(\rho\phi)}{\partial t^2}\)(d) \(-\frac{\Delta t}{2}\frac{\partial^2(\rho\phi)}{\partial t^2}\)This question was posed to me in a national level competition.The question is from Transient Flows topic in division Transient Flows of Computational Fluid Dynamics |
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Answer» CORRECT option is (d) \(-\frac{\Delta t}{2}\frac{\partial^2(\rho\phi)}{\partial t^2}\) Easiest EXPLANATION: While using the first-order explicit Euler scheme, an extra term called the numerical anti-diffusion occurs. This term can be obtained by using the Taylor SERIES EXPANSION. The term is \(-\frac{\Delta t}{2}\frac{\partial^2(\rho\phi)}{\partial t^2}\). |
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