McLachlan_BSSN.m: Add comment to explain confusing situation with advection term for \tilde \Gamma^i in \partial_t B^i equation

1 files changed, 7 insertions, 1 deletions

diff --git a/m/McLachlan_BSSN.m b/m/McLachlan_BSSN.m
index a835560..333b478 100644
--- a/m/McLachlan_BSSN.m
+++ b/m/McLachlan_BSSN.m
@@ -737,7 +737,9 @@ evolCalc =
                                  (Xt[ua] - eta BetaDriver beta[ua]))],
 
     dot[B[ua]]    -> + ShiftBCoeff (dotXt[ua] - eta BetaDriver B[ua])
-
+      (* Note that this dotXt[ua] is not yet \partial_t \tilde \Gamma^i, because the
+         advection term has not yet been added.  It is actually
+         \partial_t \tilde \Gamma^i - \beta^j \partial_j \tilde \Gamma^i *)
   }
 };
 
@@ -788,6 +790,10 @@ advectCalc =
                         + ShiftAdvectionCoeff Upwind[beta[ub], B[ua], lb]
                         + ((1 - ShiftAdvectionCoeff)
                            Upwind[beta[ub], Xt[ua], lb]))
+                      (* Note that the advection term \beta^j \partial_j \tilde \Gamma^i is not
+                         subtracted here when ShiftAdvectionCoefficient == 1 because it was
+                         implicitly subtracted before (see comment in previous calculation of
+                         dot[B[ua]]. *)
   }
 };