2014/03/17 by K. Kornet, Kornet, Kacper, Alban Pothérat +1 · 1 citation
Engineering · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.1403.4129
openalex publication_date 2014/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We put forward a new type of spectral method for the direct numerical\nsimulation of flows where anisotropy or very fine boundary layers are present.\nThe mean idea is to take advantage of the fact that such structures are\ndissipative and that their presence should reduce the number of degrees of\nfreedom of the flow, when paradoxically, their fine resolution incurs extra\ncomputational cost in most current methods. The principle of this method is to\nuse a functional basis with elements that already include these fine structure\nso as to avoid these extra costs. This leads us to develop an algorithm to\nimplement a spectral method for arbitrary functional bases, and in particular,\nnon-orthogonal ones. We construct a basic implementation of this algorithm to\nsimulate Magnetohydrodynamic (MHD) channel flows with an externally imposed,\ntransverse magnetic field, where very thin boundary layers are known to develop\nalong the channel walls. In this case, the sought functional basis can be built\nout of the eigenfunctions of the dissipation operator, which incorporate these\nboundary layers, and it turns out to be non-orthogonal. We validate this new\nscheme against numerical simulations of freely decaying MHD turbulence based on\na Finite Volume code and it is found to provide accurate results. Its ability\nto fully resolve wall-bounded turbulence with a number of modes close to that\nrequired by the dynamics is demonstrated on a simple example. This opens the\nway to full blown simulations of MHD turbulence under very high magnetic\nfields, which were until now too computationally expensive, as the\ncomputational cost of the proposed method, in contrast to traditional methods,\ndoes not depend on the intensity of the magnetic field.\n