A windowing method for periodic inflow/outflow boundary treatment of non-periodic flows. (English) Zbl 1120.76351
Summary: An inflow/outflow boundary treatment procedure is described for the numerical computation of non-periodic flows which allows for the use of periodic spatial boundary conditions. Due to this periodicity, e.g. efficient and accurate Fourier spectral methods can be applied. The governing equations of the flow are modified using window functions as known from signal processing. Thereby, the windowed solution is forced to zero to high order at the artificial boundaries. The physical solution near the boundaries is obtained by a regularised dewindowing operation and boundary conditions are imposed with the help of a suitable base flow which needs to be defined only within the window-boundary regions. On the inner domain, the unmodified flow equations are solved. The base flow can contain spatially and temporally varying disturbances. Hence it is possible to employ transitional and turbulent inflow conditions using the windowing technique.
By properly designing the window function, spectral accuracy of a Fourier discretisation can be obtained. The performance of this scheme is analysed theoretically, verified numerically and compared to the more widely used fringe region technique. It is found that the accuracy of imposing the boundary conditions is similar for both techniques. Furthermore, for flow problems with a spatially evolving base flow, the windowing method does not require the base flow to be periodic.
In this paper, the implementation of the windowing method in a two-dimensional incompressible Navier-Stokes code is examined and compared in detail to the fringe region technique for two test cases: The convection of a localised disturbance and a stationary, spatially evolving jet.
By properly designing the window function, spectral accuracy of a Fourier discretisation can be obtained. The performance of this scheme is analysed theoretically, verified numerically and compared to the more widely used fringe region technique. It is found that the accuracy of imposing the boundary conditions is similar for both techniques. Furthermore, for flow problems with a spatially evolving base flow, the windowing method does not require the base flow to be periodic.
In this paper, the implementation of the windowing method in a two-dimensional incompressible Navier-Stokes code is examined and compared in detail to the fringe region technique for two test cases: The convection of a localised disturbance and a stationary, spatially evolving jet.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
Windowing; Navier-Stokes equations; Boundary condition; Periodicity; Fourier discretisation; Fringe method; Incompressible flowReferences:
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