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solvers:ssa [Elmer/Ice Wiki]

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solvers:ssa [2013/11/25 13:34]
fgillet [SIF contents]
solvers:ssa [2017/05/19 05:20] (current)
tzwinger [General Description]
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 ==== General Informations ==== ==== General Informations ====
-:!: **important changes have been made in SSABasalSolverThis doc applies from Rev. 6440**+:!: **Important changes have been made in ''SSABasalSolver''This doc applies from Rev. 6480.**
  
   * **Solver Fortran File:** ''SSASolver.f90''   * **Solver Fortran File:** ''SSASolver.f90''
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     * (3) ''SSAFlow''     * (3) ''SSAFlow''
   * **Required Input Variable(s):**    * **Required Input Variable(s):** 
-    * (1) ''Zb'', ''Zs''+    * (1) ''Zb'', ''Zs'' and ''Effective Pressure'' when using the Coulomb type friction law
     * (2) ''Depth''      * (2) ''Depth'' 
     * (3) ''Depth'', ''FreeSurfGrad1'', ''FreeSurfGrad2'' and ''SSABasalFlow''     * (3) ''Depth'', ''FreeSurfGrad1'', ''FreeSurfGrad2'' and ''SSABasalFlow''
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 ==== General Description ==== ==== General Description ====
  
 +
 +=== Ice flow ===
  
 The ''SSABasalSolver'' solve the classical SSA equation, it has been modified in Rev. 6440 to be executed either on a grid of dimension lower than the problem dimension itself (i.e. the top or bottom grid of a 2D or 3D mesh for a SSA 1D or 2D problem), or on a grid of the same dimension of the problem (i.e. 2D mesh for a 2D plane view SSA solution). \\ The ''SSABasalSolver'' solve the classical SSA equation, it has been modified in Rev. 6440 to be executed either on a grid of dimension lower than the problem dimension itself (i.e. the top or bottom grid of a 2D or 3D mesh for a SSA 1D or 2D problem), or on a grid of the same dimension of the problem (i.e. 2D mesh for a 2D plane view SSA solution). \\
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 It will work on a 3D mesh only if the mesh as been extruded along the vertical direction and if the base line boundary conditions have been preserved (to impose neumann conditions). \\ It will work on a 3D mesh only if the mesh as been extruded along the vertical direction and if the base line boundary conditions have been preserved (to impose neumann conditions). \\
  
-The mandatory input variables are the bottom surface elevation and top surface elevation variables called **Zb** and **Zs**, respectively. \\+The mandatory input variables are the bottom surface elevation and top surface elevation variables called ''Zb'' and ''Zs'', respectively. \\
  
-For the Flow law the SSA solver use a "power-law" formulation and use the keywords //'Viscosity Exponent//', //'Critical Shear Rate'//, and //"Mean Viscosity"//. It Doesn't work with the build-in Glen's flow law (TODO).\\ +For the Flow law the SSA solver use a "power-law" formulation and use the keywords ''Viscosity Exponent'', ''Critical Shear Rate'', and ''Mean Viscosity''. It Doesn't work with the build-in Glen's flow law (TODO).\\ 
-Newton linearisation of the viscosity can be used usning the keywords //'Nonlinear System Newton After Tolerance'// and/or +Newton linearisation of the viscosity can be used using the keywords ''Nonlinear System Newton After Tolerance'and/or 
-//'Nonlinear System Newton After Iterations'//. It is automatically reset to False at the beginning of a new iteration.+''Nonlinear System Newton After Iterations''. It is automatically reset to False at the beginning of a new iteration.
    
-The //"Mean Density"// and //"Mean Viscosity"//, if not uniform along the vertical direction, can be computed using the ''GetMeanValueSolver'' routine or the "StucturedProjectToPlane" solver (prefered solution).+The ''Mean Density'' and ''Mean Viscosity'', if not uniform along the vertical direction, can be computed using the ''GetMeanValueSolver'' routine or the ''StucturedProjectToPlan'' solver (preferred solution).
  
-Contrary to the NS solver, the gravity must be orientated along the z-axis and it taken form the value of +Contrary to the NS solver, the gravity must be orientated along the z-axis and is taken from the value of 
-//''Flow BodyForce 2''// for a SSA-1D problem or //''Flow BodyForce 3''// for a SSA-2D problem.+''Flow BodyForce 2'' for a SSA-1D problem or ''Flow BodyForce 3'' for a SSA-2D problem.
  
-A Neumann condition on the lateral boundaries can be applied with the keyword //"Calving front = Logical True"// in the Bounadry condition section. The condition is : //0.5 * g * (rho_ice * h^2 - rho_water * h_im^2)// +A Neumann condition on the lateral boundaries can be applied with the keyword ''Calving front = Logical True'' in the Bounadry condition section. The condition is : //0.5 * g * (rho_ice * h^2 - rho_water * h_im^2)// 
-where +where\\ 
-  //g// is the absolute value of the gravity taken from ''Flow BodyForce i"\\ +  //g// is the absolute value of the gravity taken from ''Flow BodyForce i''\\ 
-  //rho_ice// is the ice "Mean Density"\\ +  //rho_ice// is the ice ''Mean Density''\\ 
-  //rho_water// is "water densitytaken from the "constantssection (or default=1.03225e-18)\\ +  *  //rho_water// is ''water density'' taken from the ''constants'' section (or default=1.03225e-18)\\ 
-  //h// is the front thickness computed as Zs-Zb\\ +  //h// is the front thickness computed as ''Zs-Zb''\\ 
-  //h_im// is the thickness below sea level computed as "Sea Level - Zb", where "Sea Levelis taken from the "constantssection (or default=0.0). \\ +  //h_im// is the thickness below sea level computed as ''Sea Level - Zb'', where ''Sea Level'' is taken from the ''constants'' section (or default=0.0). \\ 
-Note that in the absence of explicit boundary condition (no dirichlet condition or "Calving front = Logical Truenot found) the natural boundary condition is force equilibrium (//rho_ice * h^2 = rho_water * h_im^2//).+Note that in the absence of explicit boundary condition (no dirichlet condition or ''Calving front = Logical True'' not found) the natural boundary condition is force equilibrium (//rho_ice * h^2 = rho_water * h_im^2//).
  
-The slip coefficient coefficient values are imposed in the //Material// section with the keywords +The SSA velocities and pressure can be used, for example, as initial conditions for the Stokes Solver
-//"SSA slip coefficient i = Real ..."// with i=1,2 \\+
  
-The SSA velocities and pressure can be use, for example, as initial conditions for the Stokes Solver. \\ 
  
 +When the SSA solution is computed on a boundary of a mesh of dimension larger than the SSA problem (e.g. a 3D mesh for a SSA-2D problem), the SSA solution computed on the boundary can be
 +  * exported on the whole mesh using  the ''StructuredProjectToPlane'' solver (preffered solution) or  the  ''SSASolver'' routine \\
 +  *  used as a Dirichlet condition for the SIA velocity (see the [[solvers:sia|SIA Solver]]).
  
-When the SSA solution is computed on boundary of mesh of dimension larger than the SSA problem (e.g. a 3D mesh for a SSA-2D problem), the SSA solution computed on the boundary  +=== Basal friction === 
-  - can be exported on the whole mesh using //(i)// The "StructuredProjectToPlane" solver (prefered solutionor //(ii)// the  ''SSASolver'' routine \\ + 
-  - can be used as dirichlet condition for the SIA velocity (see the [[solvers:sia|SIA Solver]]).+Since version 6480, there are three friction laws implemented in the SSA solver:  
 + 
 +  * linear friction law 
 +  <m>  tau_b = beta . u  </m>\\ 
 +  * Weertman type friction law 
 +  <m>  tau_b = beta.{u_b}^{m - 1} u  </m>\\ 
 +  * Coulomb type friction law  
 +<m>  tau_b = 1/{A_s}^{1/n} {[{ 1/ {(1 + alpha . chi^q)} }]}^{1/n} . {u_b}^{1/n-1}. u  </m>\\ 
 +where  
 +<m>  alpha = {(q - 1)^{q-1}}/{q^q}  </m> 
 +and 
 +<m>  chi = {u_b}/{C^n N^n A_s}  </m>\\  
 +  
 +The two latests are non-linear and a Newton linearisation can be used. The friction law is chosen using the keyword ''SSA Friction Law'', which takes the value ''Linear'', ''Weertman'' or ''Coulomb''. The other keywords are:\\ 
 +  * a linear friction law 
 +    * ''SSA Friction Parameter'' -> <m>beta</m>    
 +  * Weertman type friction law 
 +    * ''SSA Friction Parameter'' -> <m>beta</m> 
 +    * ''SSA Friction Exponent'' -> <m>m</m> 
 +    * ''SSA Friction Linear Velocity'' -> <m>u_{t0}</m> 
 +  * a Coulomb type friction law      
 +    * ''SSA Friction Parameter'' -> <m>beta= {A_s}^{-m}</m> 
 +    * ''SSA Friction Exponent'' -> <m>m = 1/n</m> 
 +    * ''SSA Friction Linear Velocity'' -> <m>u_{t0}</m> 
 +    * ''SSA Friction Post-Peak'' -> <m>q >= 1</m> 
 +    * ''SSA Friction Maximum Value'' -> <m>C</m> ~ max bed slope 
 +    * ''Effective Pressure'' (variable-> <m>N</m> 
 +    * '' SSA Min Effective Pressure'' -> <m>N_{min}</m>, such that <m>N >= N_{min}</m> 
 + 
 +When  <m>u_b = (u^2+v^2)^{1/2}< u_{t0}</m>, <m>u_b</m> in the previous equations is replaced by <m>u_{t0}</m>.
  
  
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   SSA Mean Density = Real $rhoi   SSA Mean Density = Real $rhoi
  
-slip coeffs +Needed for Linear, Weertman and Coulomb  
-  SSA Slip Coefficient 1 = Real 1.0e-3 +  ! Which law are we using (linear, weertman or coulomb) 
-  SSA Slip Coefficient 2 = Real 1.0e-3+  SSA Friction Law = String "Coulomb" 
 +  ! beta parameter (beta = 1/As^m) 
 +  SSA Friction Parameter Variable coordinate 1 , Coordinate 2 
 +     Real  MATC "1.0e-3*(1.0 + sin(2.0*pi* tx(0) / L)*sin(2.0*pi* tx(1) / L)) 
 + 
 +! Needed for Weertman and Coulomb 
 +  ! Exponent m  
 +  SSA Friction Exponent = Real $1.0/n 
 +   
 +  ! Min velocity for linearisation where ub=0 
 +  SSA Friction Linear Velocity = Real 0.0001 
 + 
 +! Needed for Coulomb only 
 +  ! post peak exponent in the Coulomb law (q, in Gagliardini et al., 2007) 
 +  SSA Friction Post-Peak = Real 1.0 
 +  ! Iken's bound  tau_b/N < C (see Gagliardini et al., 2007) 
 +  SSA Friction Maximum Value = Real 0.5
 End End
 </code> </code>
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 ==== Examples ==== ==== Examples ====
-For examples look in your elmer source distribution under [ELMER_TRUNK]/elmerice/examples/Test_SSA+For examples look in your elmer source distribution under ''[ELMER_TRUNK]/elmerice/Tests/SSA'' and under ''[ELMER_TRUNK]/elmerice/examples/Test_SSA''.
solvers/ssa.1385386483.txt.gz · Last modified: 2013/11/25 13:34 by fgillet
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