Non-conservation Form With Flux Jacobians
Expanding the fluxes can be an important part of constructing numerical solvers, for example by exploiting (approximate) solutions to the Riemann problem. From the original equations as given above in vector and conservation form, the equations are written in a non-conservation form as:
where Ax, Ay and Az are called the flux Jacobians, which are matrices equal to:
Here, the flux Jacobians Ax, Ay and Az are still functions of the state vector m, so this form of the Euler equations is nonlinear, just like the original equations. This non-conservation form is equivalent to the original Euler equations in conservation form, at least in regions where the state vector m varies smoothly.
Read more about this topic: Euler Equations (fluid Dynamics)
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