Linear Instability Analysis of 3D Magnetohydrodynamic Flow by Direct Numerical Simulation


Linear Instability Analysis of 3D Magnetohydrodynamic Flow by Direct Numerical Simulation

Grants, I.; Gerbeth, G.

Direct numerical simulation (DNS) is normally used to study turbulent flows. Though, it may be also very useful for linear instability analysis of complex laminar flows. given an essentially three-dimensional basic flow the number of coupled active degrees of freedom may easily exceed 105. Calculation of the full spectrum is hardly possible if meaningful in such cases. Only a few leading modes are needed for the linear instability anaxix. Iteration techniques such as Arnold iteration may be used to find an isolated eigenvalue. A separate effort, however, is then needed to verify that this eigenvalue really has the maximum real part.
Our study demonstrates that the linear instabiolity problem can be effectively solved by means of DNS. The most straight-forward approach would be to calculate the transient equations long enough to ensure that only the leading eigenmode survives. There is, however, a more efficient way to find few leading eigenvalues and eigenmodes. this method approximates n+1 equidistant flow "snapshot" by n modes that vary exponentially in thime. We describe the numberical implementation of this method coupled with DNS and demonstrate it on an example of three-dimensional magnetohydrodynamic flow. This flow models meld motion in the Cxochralski crystal growth process with a horizontal magnetic field (HMF).

  • Contribution to proceedings
    ERCOFTAC WORKSHOP Direct and Large-Eddy Simulation 9 (DLES 9), 03.-05.04.2013, Dresden, Deutschland
    ERCOFTAC Series Volume 20: Springer, 978-3-319-14447-4, 561-567
    DOI: 10.1007/978-3-319-14448-1_71

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