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Solving 1-D Stoke's equation by finite difference method
ME605-CFD INDIAN INSTITUTE OF TECHNOLOGY GANDHINAGAR Discipline of Mechanical Engineering ME605: COMPUTATIONAL FLUID DYNAMICS COMPUTATIONAL LABORATORY 1 NUMERICAL SCHEMES FOR PARABOLIC SYSTEMS Due Date: Any time between 23-31 Aug 2014 Late submissions will attract diminishing returns! Focus: The focus of this computational laboratory session is on flow problems which are parabolic in nature. This exercise covers formulation of the flow problems in the framework of finite difference and finite volume discretization methods and the implementation of efficient and stable solution methods to salvage accurate and meaningful numerical solutions. You will use these problems to explore basic issues of numerical simulation such as convergence, error control, stability and so on covered in the associated lectures. Sample Code A Matlab code implementing the FTCS (Forward Time Central Space) scheme for the 1D parabolic PDE discussed in the lectures to model and simulate the one-dimensional heat equation is provided for you to use and modify accordingly to solve unsteady flow problems dominated by viscous diffusion. You will be required to use this code to test a Neumann boundary condition which you will develop in CA2.. 1. Brief Description of the Flow Problem The unsteady motion of the fluid due to an impulsive acceleration of an infinite flat plate in a viscous incompressible fluid can be described by 2 ??uu ?? (1) 2 ?? ty which exemplifies a parabolic equation where ? is the kinematic viscosity, u is the velocity in the x-direction. This equation implies that events propagate into the future, and a monotone convergence to steady state is expected. st Figure 1: Stokes 1 Problem This is Stokes’s first problem, a fundamental solution in fluid dynamics, which represents one of the few exact solutions to the Navier-Stokes equations. It describes the evolution of the...
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