Unstructured and multi-block structured mesh solvers

Multigrid Upwind Navier-Stokes Solver on Adaptive Unstructured Meshes

An unstructured flow solver with adaptive mesh refinement and multigrid acceleration is developed (Zheng and He 2001) to efficiently compute two-dimensional inviscid and viscous steady flows about complex configurations. High resolution is achieved by using a 2nd order upwind scheme coupled with adaptive mesh refinement. An aspect-ratio adaptive multigrid method originally developed for relaxing the time step restriction in unsteady flow computations on structured meshes (He 1993) is implemented to effectively accelerate the solution convergence of the explicit time-marching in the near wall regions with high aspect mesh ratios. The following numerical examples illustrate the capabilities of the adaptive refinement for capturing high gradient regions with shock waves for a transonic airfoil, and wake and large scale separation for low pressure turbine cascade at large negative incidence.

Unstructured mesh adaptation

 

Computation of Transonic Aerofoil

Fig 1. Computation of Transonic Aerofoil (Euler and Navier-Stokes solutions)

 

 Computation of Turbulent Flow around Low-Pressure Turbine Blades

Fig 2. Computation of Turbulent Flow around Low-Pressure Turbine Blades (large scale flow separation on pressure surface under a negative incidence)

 

Multi-Block Structured Mesh Solutions of the Navier-Stokes Equations

A multi-block solver has been developed (He, 1996), aimed at taking advantages of both the flexibility of the unstructured mesh in local refinement and he simplicity and efficiency of direct structured mesh.  The example of the multi-block mesh for the low-pressure turbine cascade is shown below.

multigrid5multigrid6multigrid7

Fig 3. Flow around Low Pressure Turbine Blades (multi-block solver)

 

References:

-Y.  Zheng and L. He, “Multigrid Upwind Euler/Navier-Stokes Computation on Adaptive Unstructured Meshes”, Aeronautical Journal, Vol.105, No.1046, pp.173-184, April, 2001.

-L. He, "New Two-Grid Acceleration Method for Unsteady Navier-Stokes Calculations", AIAA Journal of Propulsion and Power, Vol.9, No.2, pp.272-280, 1993.

-L. He, "MB3D, a multi-block 3-dimenisonal flow solver, users guide version 1’, University of Durham, 1996

-W. Ning and L. He. “Some Modelling Issues on Trailing Edge Vortex Shedding”, AIAA Journal, Vol.39, No.5, pp787-793, May, 2001.