Screenshot is from a 2048x2048 Roe scheme with superbee flux limiter of a square Sod shock tube test.
Learning about donor cell advection, slope and flux limiters. I currently have a Burgers and Roe solver with flux limiter implemented.
Sources:
- Duellemond, 2009. Lecture on Hydrodynamics II http://www.mpia-hd.mpg.de/homes/dullemon/lectures/hydrodynamicsII/
- http://www.cfdbooks.com/cfdcodes.html
- Toro, 1999, "Riemann Solvers and Numerical Methods for Fluid Dynamics"
- http://people.nas.nasa.gov/~pulliam/Classes/New_notes/euler_notes.pdf
1D:
- finish 'Backward Euler + Gauss-Seidel' & 'Riemann / Roe'
- more implicit options? fixed point? some Newton/Levenberg Marquardt/BFGS stuff?
- render as a good ol fashioned white line with circles or boxes or x's or something as gridpoints
- add a toggle for what variable is displayed
- overlay exact solution
- HLL - incorporate flux limiter so it works at all
- AMR - isn't working unless we specifically set the flux limiter to .. (donor cell?). the book says to use HLL, so get that working?
2D:
- custom inflow boundary conditions
- Von Karman vortex street demo (need viscousity, i.e. Navier-Stokes, first)
- mouse input for velocity and for boundary painting
- FBO-based advection or particle simulation for streamline tracing
- implicit Gauss-Seidel ... and then add arbitrary boundaries to it
2D-GPU
- solid: get cylinder working with Roe version
- mirror boundary conditions
- then enable hydrostatic pressure
- constant boundary options at all
- Riemann solver arbitrary boundaries
- implicit Jacobi solver
2D unstructured? 3D? 3D-GPU? 3D-unstructured? 3D-GPU-unstructured?
all:
- Entropy fix.
- CFD codes has this in euler_solver_v0.f90, Toro describes it on p.364
- Artificial viscosity
- swappable equations of state
- MHD
- ADM
- elastic solids?
- AMR
Hyperbolic Navier-Stokes: http://deepblue.lib.umich.edu/bitstream/handle/2027.42/76470/AIAA-1991-239-186.pdf http://aam.mathematik.uni-freiburg.de/IAM/Research/projectskr/motor/cnse.html