Changes between Version 28 and Version 29 of ControllingRefinement

Timestamp:

09/19/11 12:19:28 (13 years ago)

Author:

Jonathan

Comment:

—

ControllingRefinement

@@ -115 +115 @@
 [[latex($\frac{|q_{i+1}-q_{i}|}{\max \left({\frac{|q_{i+1}|+|q_{i}|}{2},\mbox{MinScale}} \right)} > \mbox{tol}$)]]
 
-and marks cell {{{i+1}}} and cell {{{i}}} for refinement.  This is essentially [[latex($\Delta x \frac{\partial log(q)}{\partial x}$)]].  The [[latex($\Delta x$)]] is for the current grid resolution and results in coarser levels being more sensitive to fluid gradients for a given tolerance.  The values of tol is found by multiplying the qTolerance for the level with the refineVariableFactor for the fluid variable and MinScale is dependent on which field you are considering.
+and marks cell {{{i+1}}} and cell {{{i}}} for refinement.  This is essentially [[latex($\Delta x \left | \frac{\partial log(|q|)}{\partial x} \right |$)]].  The [[latex($\Delta x$)]] is for the current grid resolution and results in coarser levels being more sensitive to fluid gradients for a given tolerance.  The values of tol is found by multiplying the qTolerance for the level with the refineVariableFactor for the fluid variable.  !MinScale is dependent on which field you are considering and is given in the following table:
+|| Field || !MinScale ||
+|| rho || 0.0 ||
+|| Pressure || 0.0 ||
+|| Tracer fields || [[latex($\rho$)]] ||
+|| Bx, By, Bz || [[latex($\sqrt{\rho}c_s$)]]
+|| Px, Py, Pz || [[latex($\rho c_s$)]]
+
+Note that strong adiabatic shocks will typically be resolved by a few [[latex($n$)]] cells depending on the method (PPM, PLM, etc...) and will be refined for density when [[latex($\mbox{tol} < \frac{(4-1)/n}{\frac{4+1}{2}} = \frac{3}{2.5n}= \frac{1.2}{n}$)]].  For PPM or PLM this requires tolerances < .3 or so to resolve grid aligned adiabatic shocks based on density gradients.  To resolve non-grid aligned shocks tolerances closer to .1 should be used.  ALso note that the pressure jumps will typically be much larger (of order [[latex($M^2$)]]) so pressure gradients will trigger refinement when [[latex($M > \sqrt{n\mbox{tol}}$)]].  
+
+Also note that the momentum refinement is not Galilean invariant.  But then again, neither is the numerical diffusion...
+
 
 === Changing qTolerance and !DesiredFillRatios ===