Changes between Version 65 and Version 66 of FluxLimitedDiffusion
 Timestamp:
 03/26/13 15:33:39 (12 years ago)
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FluxLimitedDiffusion
v65 v66 137 137 [[latex(R_{2,i+1/2} = \lambda_{i+1/2}+\lambda_{i+1/2}^2 R_{i+1/2}^2)]] 138 138 and 139 [[latex(R_{i+1/2} = \frac{\left  E^n_{i+1}E^n_{i} \right  }{2 \kappa_{ i+1/2} \left ( E^n_i+E^n_{i+1} \right )})]]139 [[latex(R_{i+1/2} = \frac{\left  E^n_{i+1}E^n_{i} \right  }{2 \kappa_{0R,i+1/2} \left ( E^n_i+E^n_{i+1} \right )})]] 140 140 141 141 and 142 [[latex(\kappa_{ i+1/2} = \frac{\kappa^n_{i}+\kappa^n_{i+1}}{2} \mbox{ and } \lambda_{i+1/2} = \frac{1}{R_{i+1/2}} \left ( \coth R_{i+1/2}  \frac{1}{R_{i+1/2}} \right ) )]]142 [[latex(\kappa_{0R,i+1/2} = \frac{\kappa^n_{0R,i}+\kappa^n_{0R,i+1}}{2} \mbox{ and } \lambda_{i+1/2} = \frac{1}{R_{i+1/2}} \left ( \coth R_{i+1/2}  \frac{1}{R_{i+1/2}} \right ) )]] 143 143 144 144 and … … 147 147 148 148 and 149 [[latex(R_{i} = \frac{\left  E^n_{i+1}E^n_{i1} \right  }{2 \kappa_{ i} E^n_{i}})]]149 [[latex(R_{i} = \frac{\left  E^n_{i+1}E^n_{i1} \right  }{2 \kappa_{0R,i} E^n_{i}})]] 150 150 151 151 [[CollapsibleEnd()]] … … 195 195 where the diffusion coefficient is given by 196 196 197 [[latex(\alpha_{i+1/2}=\frac{\Delta t}{\Delta x^2} \frac{c \lambda_{i+1/2}}{\kappa_{ i+1/2}} \mbox{ where } \kappa_{i+1/2} = \frac{\kappa^n_{i}+\kappa^n_{i+1}}{2} \mbox{ and } \lambda_{i+1/2} = \frac{1}{R_{i+1/2}} \left ( \coth R_{i+1/2}  \frac{1}{R_{i+1/2}} \right ) )]]197 [[latex(\alpha_{i+1/2}=\frac{\Delta t}{\Delta x^2} \frac{c \lambda_{i+1/2}}{\kappa_{0R,i+1/2}} \mbox{ where } \kappa_{0R,i+1/2} = \frac{\kappa^n_{0R,i}+\kappa^n_{0R,i+1}}{2} \mbox{ and } \lambda_{i+1/2} = \frac{1}{R_{i+1/2}} \left ( \coth R_{i+1/2}  \frac{1}{R_{i+1/2}} \right ) )]] 198 198 and where 199 [[latex(R_{i+1/2} = \frac{\left  E^n_{i+1}E^n_{i} \right  }{2 \kappa_{ i+1/2} \left ( E^n_i+E^n_{i+1} \right )})]]199 [[latex(R_{i+1/2} = \frac{\left  E^n_{i+1}E^n_{i} \right  }{2 \kappa_{0R,i+1/2} \left ( E^n_i+E^n_{i+1} \right )})]] 200 200 201 201