Abstract
The set of equations governing the viscous incompressible fluid motion under the influence of an external MF are the momentum and mass conservation equations, given by
where \(\mathbb {S}\) is the viscous stress tensor written as
with density \(\rho \), pressure p and dynamics viscosity \(\mu \). \({\varvec{F}}_{s}\) stands for the surface tension which just acts on the interface and is formulated as a volume force based on the CSF technique.
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References
Müller U, Bühler L (2013) Magnetofluiddynamics in channels and containers. Springer Science and Business Media, Berlin
Ni MJ, Munipalli R, Morley NB et al (2007) A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: on a rectangular collocated grid system. J Comput Phys 227(1):174–204
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Zhang, J. (2019). Governing Equations. In: The Developments and the Applications of the Numerical Algorithms in Simulating the Incompressible Magnetohydrodynamics with Complex Boundaries and Free Surfaces. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-6340-4_2
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DOI: https://doi.org/10.1007/978-981-10-6340-4_2
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