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This SIA solver is not classical in that sense that the equations are not solved on a grid of dimension lower than the problem dimension itself. The geometry (H, B and S) is here given by the mesh. For a flow line problem, the mesh is a plane surface, and a volume for a 3D problem. Regarding this aspect, this solver is certainly not as efficient as a classical SIA solver. But, on the other hand, it works for unstructured grid and non-constant viscosity. The SIA velocities and pressure can be use, for example, as initial conditions for the Stokes Solver. Contrary to the NS solver, the gravity must be orientated along the z-axis.
The SIA solver uses the same input parameters as the NS solver (Viscosity, Density, Viscosity Exponent, Flow BodyForce,…).
The basal velocities are given as Dirichlet BC on the bedrock surface. The SSA Solver can be used to this purpose.
The required keywords in the SIF file for this solver are:
Solver 1 Equation = String "StressSolver" Procedure = File "ComputeDevStressNS" "ComputeDevStress" ! this is just a dummy, hence no output is needed !----------------------------------------------------------------------- Variable = -nooutput "Sij" Variable DOFs = 1 ! the name of the variable containing the flow solution (U,V,W,Pressure) !----------------------------------------------------------------------- Flow Solver Name = String "Flow Solution" ! the name of the stress solution (default is 'stress') Stress Variable Name = String 'Sigma' !----------------------------------------------------------------------- Exported Variable 1 = "Sigma" ! [Sxx, Syy, Szz, Sxy] in 2D ! [Sxx, Syy, Szz, Sxy, Syz, Szx] in 3D Exported Variable 1 DOFs = 6 ! 4 in 2D, 6 in 3D Linear System Solver = "Iterative" Linear System Iterative Method = "BiCGStab" Linear System Max Iterations = 300 Linear System Convergence Tolerance = 1.0E-09 Linear System Abort Not Converged = True Linear System Preconditioning = "ILU0" Linear System Residual Output = 1 End Material 1 ... ! we want to have the Cauchy stress !---------------------------------- Cauchy = Logical True End
Download an example using this solver. TODO
When used this solver can be cited using the following references:
Gagliardini O., D. Cohen, P. Råback and T. Zwinger, 2007. Finite-Element Modeling of Subglacial Cavities and Related Friction Law. J. of Geophys. Res., Earth Surface, 112, F02027.