Transient incompressible flow - CBS Algorithm

CBS nsteps #(in)
deltaT #()
[theta1 #(in)]
[theta2 #(in)]
[cmflag #(in)]
[scaleflag #(in) lscale #(in) uscale #(in) dscale #(in)]
[lstype #(in)] [smtype #(in)]

Solves the transient incompressible flow using algorithm based on Characteristics Based Split (CBS, for reference see O.C.Zienkiewics and R.L.Taylor: The Finite Element Method, 3rd volume, Butterworth-Heinemann, 2000). At present, only semi-implicit form of the algorithm is available and energy equation, yielding the temperature field, is not solved. Parameter nsteps determines number of solution steps. Parameter deltaT is time step length used for integration. This time step will be automatically adjusted to satisfy integration stability limits $ \Delta t \le {\frac{h}{\vert\boldsymbol{u}\vert}}$ and $ \Delta t \le {\frac{h^2}{2\nu}}$, if necessary. Parameters theta1 and theta2 are integration constants, $ \theta_1, \theta_2 \in \langle{\frac12}, 1\rangle$. If cmflag is given a nonzero value, then consistent mass matrix will be used instead of (default) lumped one.

The characteristic equations can be solved in non-dimensional form. To enable this, the scaleflag should have a nonzero value, and the following parameters should be provided: lscale, uscale, and dscale representing typical length, velocity, and density scales.

Parameter lstype allows to select solver for linear system of equations. Parameter smtype allows to select sparse matrix storage scheme. The scheme should be compatible with solver type. See section 5.1 for further details.

Borek Patzak