## Abstract

The influence of uniform magnetic fields on stationary simultaneous solutions in a channel with sudden expansion is studied in this work. Reynolds number (Re) values between 250 ≤ Re ≤ 550 and magnetic fields with Hartmann numbers (Ha) between 0 ≤ Ha ≤ 100 are considered. The global meshless method of approximate particular solutions (MAPS) is implemented to obtain the simultaneous stationary solutions that are presented in Re values above an approximate critical value of Re _{c} ≈ 219. The base functions used in the MAPS to approximate velocity and pressure fields solve an auxiliary Stokes system. The four-sided lid-driven cavity (4SLDC) and backward facing step flows are considered as validation problems in order to show the ability of the method to study bifurcations and solve magnetohydrodynamic problems, respectively. The influence of transverse magnetic fields on the sudden expansion flow for low Ha contrasts with the few effects that a stream-wise field produces. The asymmetric flow is eliminated if a transverse magnetic field with Ha = 5 is imposed over the flow and recirculation zones almost disappear at Ha = 20 for Re values considered in this work.

Original language | English |
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Article number | 051416 |

Journal | Fluid Dynamics Research |

Volume | 50 |

Issue number | 5 |

DOIs | |

State | Published - 29 Aug 2018 |

### Bibliographical note

Funding Information:This work was supported by COLCIENCIAS by means of the PhD student supporting program.

Publisher Copyright:

© 2018 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

## Keywords

- meshless methods
- MHD
- stationary bifurcation
- stokes particular solutions

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