Changes between Version 100 and Version 101 of FluxLimitedDiffusion

Timestamp:

03/28/13 11:44:44 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -312 +312 @@
 
 || Numerical value  ||  Boundary                  ||  [[latex(E^{n+1}_{i+1})]]        ||  [[latex(E^{n+1}_i)]]                         ||   [[latex(E^{n+1}_{i-1})]]                       ||  [[latex(S)]] 
-||  0               ||  RAD_FREE_STREAMING        ||  [[latex(0)]]                    ||  [[latex(\psi c \frac{\Delta t}{\Delta x})]]  ||  [[latex(-\psi\alpha_{i-1/2})]]  ||  [[latex(-\bar{\psi}c \frac{\Delta t}{\Delta x} E^n_i)]]    || 
+||  0               ||  RAD_FREE_STREAMING        ||  [[latex(0)]]                    ||  [[latex(\psi c \frac{\Delta t}{\Delta x})]]  ||  [[latex(-\psi\alpha_{i-1/2})]]  ||  [[latex(-\bar{\psi}c \frac{\Delta t}{\Delta x} E^n_i) + \bar{\psi}\alpha_{i-1/2} \left ( E^n_{i-1}-E^n_i \right )]]    || 
 ||  1               ||  RAD_EXTRAPOLATE_FLUX     ||  [[latex(0)]]                    ||  [[latex(0)]]                                 ||  [[latex(0)]]  ||  [[latex(0)]]    ||
-||  2               ||  INTERNAL/PERIODIC         ||  [[latex(-\psi\alpha_{i+1/2})]]  ||  [[latex(\psi\alpha_{i+1/2})]]                ||  [[latex(-\psi\alpha_{i-1/2})]]  ||  [[latex(\bar{\psi}\alpha_{i+1/2} \left ( E^n_{i+1}-E^n_i \right ))]]  ||
-||  3               ||  RAD_REFLECTING            ||  [[latex(0)]]                    ||  [[latex(0)]]                                 ||  [[latex(-\psi\alpha_{i-1/2})]]  ||  [[latex(0)]]    ||
-||  4               ||  RAD_USERDEFINED_BOUNDARY/AMR_BOUNDARY  ||  [[latex(0)]]       ||  [[latex(\psi\alpha_{i+1/2})]]                ||  [[latex(-\psi\alpha_{i-1/2})]]  ||   [[latex(\bar{\psi}\alpha_{i+1/2} \left ( E^n_{i+1}-E^n_i \right ) - \psi \alpha_{i+1/2} E^{n+1}_{i+1} )]]   ||
-||  5               ||  RAD_USERDEFINED_FLUX      ||  [[latex(0)]]                    ||  [[latex(0)]]                                 ||   [[latex(-\psi\alpha_{i-1/2})]]  ||    [[latex(F_0 \frac{\Delta t}{\Delta x})]]   ||
-
- !* Also requires zeroing out stencil and source contributions from [[latex(E^{n+1}_{i-1} \mbox{ and } E^n_{i-1})]] 
+||  2               ||  INTERNAL/PERIODIC         ||  [[latex(-\psi\alpha_{i+1/2})]]  ||  [[latex(\psi\alpha_{i+1/2})]]                ||  [[latex(-\psi\alpha_{i-1/2})]]  ||  [[latex(\bar{\psi}\alpha_{i+1/2} \left ( E^n_{i+1}-E^n_i \right ) + \bar{\psi}\alpha_{i-1/2} \left ( E^n_{i-1}-E^n_i \right ))]]  ||
+||  3               ||  RAD_REFLECTING            ||  [[latex(0)]]                    ||  [[latex(0)]]                                 ||  [[latex(-\psi\alpha_{i-1/2})]]  ||  + \bar{\psi}\alpha_{i-1/2} \left ( E^n_{i-1}-E^n_i \right )    ||
+||  4               ||  RAD_USERDEFINED_BOUNDARY/AMR_BOUNDARY  ||  [[latex(0)]]       ||  [[latex(\psi\alpha_{i+1/2})]]                ||  [[latex(-\psi\alpha_{i-1/2})]]  ||   [[latex(\bar{\psi}\alpha_{i+1/2} \left ( E^n_{i+1}-E^n_i \right ) - \psi \alpha_{i+1/2} E^{n+1}_{i+1} + \bar{\psi}\alpha_{i-1/2} \left ( E^n_{i-1}-E^n_i \right ))]]   ||
+||  5               ||  RAD_USERDEFINED_FLUX      ||  [[latex(0)]]                    ||  [[latex(0)]]                                 ||   [[latex(-\psi\alpha_{i-1/2})]]  ||    [[latex(F_0 \frac{\Delta t}{\Delta x} + \bar{\psi}\alpha_{i-1/2} \left ( E^n_{i-1}-E^n_i \right ))]]   ||
+
+
 
 
@@ -554 +554 @@
 === Summary ===
 
+
+|| Numerical value  ||  Boundary                  ||  [[latex(E^{n+1}_{i+1})]]        ||  [[latex(E^{n+1}_i)]]                         ||   [[latex(E^{n+1}_{i-1})]]                       ||  [[latex(S)]] 
+||  0               ||  RAD_FREE_STREAMING        ||  [[latex(0)]]                    ||  [[latex(\psi c \frac{\Delta t}{\Delta x})]]  ||  [[latex(-\psi\alpha_{i-1/2})]]  ||  [[latex(-\bar{\psi}c \frac{\Delta t}{\Delta x} E^n_i) + \bar{\psi}\alpha_{i-1/2} \left ( E^n_{i-1}-E^n_i \right )]]    || 
+||  1               ||  RAD_EXTRAPOLATE_FLUX     ||  [[latex(0)]]                    ||  [[latex(0)]]                                 ||  [[latex(0)]]  ||  [[latex(0)]]    ||
+||  2               ||  INTERNAL/PERIODIC         ||  [[latex(-\psi\alpha_{i+1/2})]]  ||  [[latex(\psi\alpha_{i+1/2})]]                ||  [[latex(-\psi\alpha_{i-1/2})]]  ||  [[latex(\bar{\psi}\alpha_{i+1/2} \left ( E^n_{i+1}-E^n_i \right ) + \bar{\psi}\alpha_{i-1/2} \left ( E^n_{i-1}-E^n_i \right ))]]  ||
+||  3               ||  RAD_REFLECTING            ||  [[latex(0)]]                    ||  [[latex(0)]]                                 ||  [[latex(-\psi\alpha_{i-1/2})]]  ||  + \bar{\psi}\alpha_{i-1/2} \left ( E^n_{i-1}-E^n_i \right )    ||
+||  4               ||  RAD_USERDEFINED_BOUNDARY/AMR_BOUNDARY  ||  [[latex(0)]]       ||  [[latex(\psi\alpha_{i+1/2})]]                ||  [[latex(-\psi\alpha_{i-1/2})]]  ||   [[latex(\bar{\psi}\alpha_{i+1/2} \left ( E^n_{i+1}-E^n_i \right ) - \psi \alpha_{i+1/2} E^{n+1}_{i+1} + \bar{\psi}\alpha_{i-1/2} \left ( E^n_{i-1}-E^n_i \right ))]]   ||
+||  5               ||  RAD_USERDEFINED_FLUX      ||  [[latex(0)]]                    ||  [[latex(0)]]                                 ||   [[latex(-\psi\alpha_{i-1/2})]]  ||    [[latex(F_0 \frac{\Delta t}{\Delta x} + \bar{\psi}\alpha_{i-1/2} \left ( E^n_{i-1}-E^n_i \right ))]]   ||
+
+
 || Numerical value  ||  Boundary                  ||  [[latex(E^{n+1}_{i+1})]]        ||  [[latex(E^{n+1}_i)]]                         ||   [[latex(E^{n+1}_{i-1})]]                       ||  [[latex(S)]] 
 ||  0               ||  RAD_FREE_STREAMING        ||  [[latex(0)]]                    ||  [[latex(\psi c \frac{\Delta t}{\Delta x})]]  ||  [[latex(-\psi\alpha_{i-1/2})]]  ||  [[latex(-\bar{\psi}c \frac{\Delta t}{\Delta x} E^n_i)]]    ||