A High-Order Unstaggered Constrained-Transport Method for the Three-Dimensional Ideal Magnetohydrodynamic Equations Based on the Method of Lines

2013 ◽  
Vol 35 (2) ◽  
pp. A623-A651 ◽  
Author(s):  
Christiane Helzel ◽  
James A. Rossmanith ◽  
Bertram Taetz
Keyword(s):  
Method Of Lines ◽  
Three Dimensional ◽  
High Order ◽  
Magnetohydrodynamic Equations ◽  
The Method Of Lines ◽  
Ideal Magnetohydrodynamic ◽  
Constrained Transport ◽  
Transport Method

scholarly journals Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients

1995 ◽  
Vol 41 (138) ◽  
pp. 333-344 ◽  
Author(s):  
Heinz Blatter
Keyword(s):  
Method Of Lines ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Velocity Fields ◽  
Deviatoric Stress ◽  
Shear Stresses ◽  
Algebraic Equations ◽  
Field Equations ◽  
Stress Gradients ◽  
The Method Of Lines

AbstractA new and efficient algorithm for computing the three-dimensional stress and velocity fields in grounded glaciers includes the role of deviatoric stress gradients. A consistent approximation of first order in the aspect of ratio of the ice mass gives a set of eight field equations for the five stress and three velocity components and the corresponding boundary conditions. A coordinate transformation mapping the local ice thickness on to unity and approximating the derivatives in the horizontal direction by centered finite-differences yields five ordinary differential and three algebraic equations. This allows use of the method of lines, starting the integration with prescribed stress and velocity components at the base, and a simple iteration procedure converges rapidly.The algorithm can be used for a wide rangе of stress-strain-rate relations, as long as strain only depends on deviatoric and shear stresses and on temperature. Sensitivity tests using synthetic and realistic ice geometries show the relevance of normal deviatoric stresses in the solutions for the velocity components even for ice sheets. Stress and velocity fields may deviate substantially from the widely used shallow-ice approximation.

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