Fix deviatoric stress in some examples (#24)

* Correct trace for 2-D compressible flow examples

* remove trace in wang_etal_2024

Author: cmdoug

examples/brokof_etal_2024/eqns_brokof_etal_2024.idp

@@ -17,8 +17,7 @@
   macro ugradu(v, U, u) ( v  *(U*dX(u  ) + U#y*dy(u  ) )
                         + v#y*(U*dX(u#y) + U#y*dy(u#y) ) ) // scaled convection term
 
-  macro visc(v, u) ( dX(v  )*(2.0*dX(u) - 2./3.*div(u)) + dy(v  )*(dX(u#y) + dy(u)             )
-                   + dX(v#y)*(dX(u#y) + dy(u))          + dy(v#y)*(2.0*dy(u#y) - 2./3.*div(u)) ) // EOM
+  macro visc(v, u) ( dX(v)*(dX(u) - dy(u#y)) + (dy(v) + dX(v#y))*(dX(u#y) + dy(u)) + dy(v#y)*(dy(u#y) - dX(u)) ) // EOM
 
   macro diff(g, f) ( dX(g)*dX(f) + dy(g)*dy(f) ) // EOM
 

examples/fani_etal_2018/eqns_fani_etal_2018.idp

@@ -13,7 +13,7 @@
   macro vdotu(v, u) ( v*u + v#y*u#y ) // velocity inner product
   macro div(u) ( dx(u) + dy(u#y) ) // velocity divergence
   macro ugradu(v, U, u) ( v*(U*dx(u) + U#y*dy(u)) + v#y*(U*dx(u#y) + U#y*dy(u#y)) ) // velocity advection term
-  macro visc(v, u) ( 2.*dx(v)*(dx(u) - 1./3.*div(u)) + dy(v)*(dx(u#y) + dy(u)) + dx(v#y)*(dx(u#y) + dy(u)) + 2.*dy(v#y)*(dy(u#y) - 1./3.*div(u)) ) // viscous term
+  macro visc(v, u) ( dx(v)*(dx(u) - dy(u#y)) + (dy(v) + dx(v#y))*(dx(u#y) + dy(u)) + dy(v#y)*(dy(u#y) - dx(u)) ) // viscous term
   macro diff(g, f) ( dx(g)*dx(f) + dy(g)*dy(f) ) // scalar diffusion term
   macro ugradf(U, f)   ( U*dx(f) + U#y*dy(f) ) // scalar advection term
 // Boundary conditions

examples/wang_etal_2024/eqns_wang_etal_2024.idp

@@ -22,8 +22,8 @@
   macro ugradu(v, U, u) ( y*(v  *(U*dx(u  ) + U#y*dy(u  ))
                            + v#y*(U*dx(u#y) + U#y*dy(u#y))) ) // scaled convection term
 
-  macro visc(v, u) ( 2.*y*dx(v)*dx(u)               +     y*dy(v)*(dx(u#y) + dy(u))
-                      + y*dx(v#y)*(dx(u#y) + dy(u)) + 2.*(y*dy(v#y)*dy(u#y) + v#y*u#y/y) ) // EOM
+  macro visc(v, u) ( 2.*dx(v)*(y*dx(u) - div(u)/3.) + y*(dy(v) + dx(v#y))*(dx(u#y) + dy(u))
+                   + 2.*(dy(v#y)*(y*dy(u#y) - div(u)/3.) + v#y*(u#y/y - div(u)/3.)) ) // EOM
 
   macro diff(g, f) ( y*(dx(g)*dx(f) + dy(g)*dy(f)) ) // EOM