Changes between Version 65 and Version 66 of SelfGravityDevel


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Timestamp:
10/22/19 12:31:08 (5 years ago)
Author:
Jonathan
Comment:

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  • SelfGravityDevel

    v65 v66  
    2424AstroBEAR uses hypre's linear solver to solve Poisson's equation for the potential.  However, there are two methods for including the source terms for momentum and energy.  The non-conservative approach simply includes the terms during a source update, while the conservative approach recasts the RHS of the momentum and energy equations as total divergences - so they can be differenced conservatively.
    2525
    26 Substituting the Poisson equation into the momentum equation we have
    27 
    28 [[latex($\frac{d \rho \mathbf{v}}{dt} = (\frac{\nabla^2\phi}{4 \pi G}+\rho_0) \nabla \phi = \nabla \cdot \left [ \frac{1}{4 \pi G} \left ( \nabla \phi \nabla \phi - \frac{1}{2} \left ( \nabla \phi \cdot \nabla \phi + 4 \pi G \rho_0 \phi \right) \right ) \right ]$)]]
    29 
     26Substituting the Poisson equation into the momentum equation we have after some manipulations
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     28
     29[[latex($\frac{d \rho \mathbf{v}}{dt} = (\frac{\nabla^2\phi}{4 \pi G}+\rho_0) \nabla \phi = \nabla \cdot \left [ \frac{1}{4 \pi G} \left ( \nabla \phi \nabla \phi - \frac{1}{2} \left ( \nabla \phi \cdot \nabla \phi \right) + \rho_0 \phi \right ) \right ]$)]]
     30
     31where we have the momentum flux tensor
     32
     33[[latex($\mathbf{T} =  \frac{1}{4 \pi G} \left ( \nabla \phi \nabla \phi - \frac{1}{2} \left ( \nabla \phi \cdot \nabla \phi + 4 \pi G \rho_0 \phi \right) \right )$)]]
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