Transient transport problem - linear case

NonStationaryProblem nsteps #(in)
deltaT #(rn) $ \vert$ deltaTfunction #(in)
alpha #(rn)
[initT #(rn)]
[sparselinsolverparams #(..)]
[exportfields #(ia)]

Linear implicit integration scheme for transient transport problems. The generalized midpoint rule (sometimes called $ \alpha$-method) is used for time discretization, with alpha parameter, which has limits $ 0\le\alpha\le1$. For $ \alpha=0$ explicit Euler forward method is obtained, for $ \alpha=0.5$ implicit trapezoidal rule is recovered, which is unconditionally stable, second-order accurate in $ \Delta t$, and $ \alpha=1.0$ yields implicit Euler backward method, which is unconditionally stable, and first-order accurate in $ \Delta t$. deltaT is time step length used for integration, nsteps parameter specifies number of time steps to be solved. It is possible to define deltaTfunction with a number referring to corresponding time function, see section 4.10. Variable time step is advantageous when calculating large time intervals. It is strongly suggested to use nonlinear transport solver due to stability reasons, see section 3.2.3.

The initT sets the initial time for integration, 0 by default. If lumpedcapa is set, then the stabilization of numerical algorithm using lumped capacity matrix will be used, reducing the initial oscillations. See section 3.2.1 for an explanation on exportfields.

This linear transport problem supports changes in number of equations. It is possible to impose/remove Dirichlet boundary conditions during solution. This feature is enabled with changingProblemSize, which ensures storing solution values on nodes (DoFs) directly. If the problem does not grow/decrease during solution, it is more efficient to use conventional solution strategy and the parameter should not be mentioned.

Note: This problem type requires transport module and it can be used only when this module is included in your oofem configuration.

Borek Patzak