# EllipSys3D ABL

The EllipSys3D code is a multiblock finite volume discretization of the incompressible Reynolds Averaged Navier-Stokes (RANS) equations in general curvilinear coordinates.  The code uses a collocated variable arrangement, and Rhie/Chow interpolation [iv] is used to avoid odd/even pressure decoupling. As the code solves the incompressible flow equations, no equation of state exists for the pressure, and the SIMPLE algorithm of [v] is used to enforce the pressure/velocity coupling. The EllipSys3D code is parallelized with MPI for executions on distributed memory machines, using a non-overlapping domain decomposition technique.

The solution is advanced in time using a 2nd order iterative time-stepping (or dual time-stepping) method.  In each global time-step the equations are solved in an iterative manner, using under-relaxation. First, the momentum equations are used as a predictor to advance the solution in time.  At this point in the computation the flowfield will not fulfil the continuity equation. The rewritten continuity equation (the so called pressure correction equation) is used as a corrector making the predicted flowfield satisfy the continuity constraint.  This two step procedure corresponds to a single sub-iteration, and the process is repeated until a convergent solution is obtained for the timestep. When a convergent solution is obtained, the variables are updated, and we continue with the next timestep.

The three momentum equations are solved decoupled using a red/black Gauss-Seidel point solver. The solution of the Poisson system arising from the pressure correction equation is  accelerated using a multigrid method. In order to accelerate the overall algorithm, a three level grid sequence and local time stepping are used.

## EllipSys3D ABL

Submitted by Tilman Koblitz on May 4, 2015 - 5:49pm
Main hypothesis

The EllipSys3D code is a multiblock finite volume discretization of the incompressible Reynolds Averaged Navier-Stokes (RANS) equations in general curvilinear coordinates.  The code uses a collocated variable arrangement, and Rhie/Chow interpolation [iv] is used to avoid odd/even pressure decoupling. As the code solves the incompressible flow equations, no equation of state exists for the pressure, and the SIMPLE algorithm of [v] is used to enforce the pressure/velocity coupling. The EllipSys3D code is parallelized with MPI for executions on distributed memory machines, using a non-overlapping domain decomposition technique.

The solution is advanced in time using a 2nd order iterative time-stepping (or dual time-stepping) method.  In each global time-step the equations are solved in an iterative manner, using under-relaxation. First, the momentum equations are used as a predictor to advance the solution in time.  At this point in the computation the flowfield will not fulfil the continuity equation. The rewritten continuity equation (the so called pressure correction equation) is used as a corrector making the predicted flowfield satisfy the continuity constraint.  This two step procedure corresponds to a single sub-iteration, and the process is repeated until a convergent solution is obtained for the timestep. When a convergent solution is obtained, the variables are updated, and we continue with the next timestep.

The three momentum equations are solved decoupled using a red/black Gauss-Seidel point solver. The solution of the Poisson system arising from the pressure correction equation is  accelerated using a multigrid method. In order to accelerate the overall algorithm, a three level grid sequence and local time stepping are used.

Software
Solver
EllipSys3D
Regime
Turbulence
Turbulence closure
Turbulence model

modified k-epsilon model

Atmospheric boundary layer
Range
Coriolis
Yes
Atmospheric Stability
Atmospheric Stability
Yes
Canopy
Forest canopy
No
Wind farm
Wind turbine
No
References

[i] Michelsen J.A., ”Basis3D - a Platform for Development of Multiblock PDE Solvers” Technical Report AFM 92-05, Technical University of Denmark, 1992.

[ii] Michelsen J.A., ”Block structured Multigrid solution of 2D and 3D elliptic PDE's”, Technical Report AFM 94-06, Technical University of Denmark, 1994.

[iii] Sørensen N.N., ”General Purpose Flow Solver Applied to Flow over Hills”, Risø-R-827-(EN), Risø National Laboratory, Roskilde, Denmark, June 1995.

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