could you please help me with this assignment the model is CFD ( computational f
ID: 3278542 • Letter: C
Question
could you please help me with this assignment the model is CFD ( computational fluid dynamic) Dirichlet boundary Give the Finite Volume Discretisation for piai-(IVo) Start with the incomplete fom ,(ai), .4, , (Ve), *4, and apply the general face value interpolation rule e, =B,9, + (1-a,eN. Derive the coefficents al, a. a,and s, that will satisfy @per-arPk +@g#x + Sr for the computational molecule shown in the figure. k 9P ax 2. Von Neumann boundary Gve the Finite Volume Discretisation for .pai-(IV. Start with the incomplete fom (ai), * A,-T, (ve), *4, and apply upwind dnerencing for the face value interpolation. Derive the coefficients a a, and s, that wil satsfy = arPr + aw#x + Sr for the computational molecule shown in the figure below. op 9p PE oxExplanation / Answer
When using a Dirichlet boundary condition, one prescribes the value of a variable at the boundary, e.g. u(x) = constant. • When using a Neumann boundary condition, one prescribes the gradient normal to the boundary of a variable at the boundary, e.g. nu(x) = constant. • When using a mixed boundary condition a function of the form au(x)+b nu(x) = constant is applied. • Note that at a given boundary, different types of boundary conditions can be used for different variables.
Boundary conditions are generally obtained by setting the velocity at the boundary equal to the velocity of the surface (called the no slip condition). In the case of the spheres, suppose the radius of the small sphere is rr, the large sphere is RR, the oscillations described by asin(t)asin(t) along the xxdirection, then, assuming the center of the large sphere to be the origin, the boundary conditions will be :
uxt=acos(t),uyt=0,uzt=0at(xasin(t))2+y2+z2r2=0uxt=acos(t),uyt=0,uzt=0at(xasin(t))2+y2+z2r2=0
and
uxt=0,uyt=0,uzt=0atx2+y2+z2R2=0uxt=0,uyt=0,uzt=0atx2+y2+z2R2=0
where the symbols have their usual meanings. although the second condition is a familiar Dirichlet type boundary condition, the first condition is a bit more rare and may be more difficult to apply when talking about numerical simulations, since much less is studied about it.
In the case of the free surface, the conditions at the surface will have a similar form though the exact equation will depend on the details.
Summary • Zones are used to assign boundary conditions. • Wide range of boundary conditions permit flow to enter and exit solution domain. • Wall boundary conditions used to bound fluid and solid regions. • Repeating boundaries used to reduce computational effort. • Internal cell zones used to specify fluid, solid, and porous regions. • Internal face boundaries provide way to introduce step change in flow properties.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.