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涡量-流函数方法(附Fotran程序)
徐翱
Vorticity-Streamfunction Method for
Buoyancy Driven Cavity Probelm
Key words : vorticity-streamfunction method; buoyancy driven cavity flow
1. Problem
The dimensionless governing equations are:
where, streamfunction is defined as ,
Vorticity (in Left hand cartesian system) is defined as
Initial boundary condition set as:
徐翱
2. Numerical Scheme
2.1 Mesh generation
Uniform mesh is used as
2.2 Discretization
2.2.1 Discretize the vorticity equation at all the interior points, for spatial discretization using
central discretization scheme and for time discretization using explicit time advance method
(Euler method).
2.2.2 Discretize the streamfunction equation using central difference scheme
Employing implicit methd, Setting , then get
Where
徐翱
2.2.3 For velocity components,
2.2.4 Energy equation is solved in the same way as vorticity equation:
2.3 Boundary condition
2.3.1 Implementation of voticity condition using Taylor series expansion with 2nd order
approximation:
2.3.2 Implementation of streamfunction condition using 2nd order finite difference scheme to
approximate the derivative condition:
,etc.
2.3.3 Implementation of temperature condition
2.4 Flow chat
徐翱
Solve vorticity
equation
Compute Solve
temperature field streamfunction
equation
Compute velocity Update
streamfunction at
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