A New High-Order Method for the Accurate Simulation of Incompressible Wall-Bounded Flows
A new high-order method for the accurate simulation of incompressible wall-bounded flows is presented. In stream- and spanwise direction the discretisation is performed by standard Fourier series, while in wall-normal direction the method combines high-order collocated compact finite differences with the influence matrix method to calculate the pressure boundary conditions that render the velocity field divergence-free. The main advantage over Chebyshev collocation is that in wall-normal direction, the grid can be chosen freely and thus excessive clustering near the wall is avoided. Both explicit and implicit discretisations of the viscous terms are described, with the implicit method being more complex, but also having a wider range of applications. The method is validated by simulating fully turbulent channel flow at friction Reynolds number \(Re_\tau = 395\), and comparing our data with existing numerical results. The results show excellent agreement proving that the method simulates all physical processes correctly.
KeywordsDirect Numerical Simulation Spanwise Direction Turbulent Channel Flow Pressure Boundary Condition Compact Finite Difference Scheme
Financial support from the Swedish Research Council and computer time provided by SNIC (Swedish National Infrastructure for Computing) is gratefully acknowledged.
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