Investigation of micro-shock waves in a planar magnetogasdynamic flow using the discontinuous Galerkin finite element method

Abstract

The present work focuses on the numerical investigation of micro-shock wave propagation in a two-dimensional magnetogasdynamic flow in the framework of the Dis- continuous Galerkin-Finite Element Method (DG-FEM). The Lorentz force has been im- plemented in the compressible, viscous Navier–Stokes equations as a source term using first-order spatial and fourth-order temporal Runge–Kutta discretization schemes. To in- vestigate the effect of the electrical conductivity on the micro-shock wave propagation, a two-dimensional micro-shock channel problem with hydraulic diameter of 2.5 mm, length of 82 mm, and no-slip boundary conditions at the left and at the right wall is considered as a benchmark problem. In this case, acoustic waves are generated behind after the rupture of the membrane that separates two states of the same gas originally at different pressure and density and both initially at rest. The magnetic field is taken into account as uniform and stationary throughout the microchannel, and the numerical simulations are performed in a short physical time, before the reflection of the waves on the lateral wall. A detailed parametric study of the temperature, density, pressure, and u-velocity is carried out by a variation of the electrical conductivity of the magnetogasdynamic flow, under the assumption of low magnetic Reynolds numbers. It has been found that the jumps of the acoustic waves become significantly intensified when the electrical conductivity of the gas is increased. It has also been observed that the presence of the Lorentz force causes an acceleration in the gasflow towards the outlet section of the microchannel at the low Knudsen number of 0.05. The outcome of this research work could be relevant to biomedical applications where the ability to control the flow in a microchannel has a significant impact on the development of small devices aimed to deliver pharmaceutical drugs in specific locations.