Exploring the Atwood number impact on shock-driven hydrodynamic instability at pentagonal interface using discontinuous Galerkin simulations

Physica D Nonlinear Phenomena, vol. 467, pp. 134276

Abstract

Investigation of Atwood number impact is crucial for comprehending the flow dynamics of the evolving hydrodynamic instability. In this paper, the Atwood number impacts on the shock-driven hydrodynamic instability at a backward-facing pentagonal interface in its early stages are explored numerically. The shock-driven pentagonal interface has a unique property in which the incident angle of the shock wave is constant along the interface edge. This property provides the ideal environment for the shock-refraction process. To examine the Atwood number impact, we consider five distinct gases, including sulfur hexafluoride, krypton, argon, neon, and helium, which are filled inside the pentagonal interface and surrounded by nitrogen gas. A mixed modal discontinuous Galerkin method is used to solve the two-dimensional Navier–Stokes–Fourier equations for two-component gas flows for numerical simulations. The simulation results illustrate that the Atwood number plays a crucial role in the flow fields of the shocked-pentagonal gas interface, which have not been reported in the literature. The flow fields are greatly impacted by the Atwood number, leading to complex wave patterns, shock focusing, jet formation, interface deformation, and vorticity generation. Further, the Atwood number effects on the flow fields are also thoroughly examined by a quantitative study based on the integral quantities and the interface features. Finally, a quantitative analysis is performed to examine the intrinsic differences between the evolution of the flow fields at the square and pentagonal interfaces.

Authors 4

1. Sham Bansal

   D.B.S. (P.G.) College, Dehradun

   Affiliation as printed

   Department of Mathematics, D.B.S. (P.G.) College (Dehradun), H.N.B. Garhwal Central University, Uttarakhand, India

   Department of Mathematics, Mata Gujri College, Fatehgarh Sahib, Punjab, India

2. Akshay Saini

   Hemwati Nandan Bahuguna Garhwal University

   Affiliation as printed

   Department of Mathematics, H.N.B. Garhwal University (A Central University), Srinagar, Uttarakhand, India

3. Anup Singh Negi

   Graphic Era Hill University

   Affiliation as printed

   Department of Allied Sciences (Mathematics), Graphic Era Hill University, Dehradun, Uttarakhand, India

4. Satyvir Singh corresponding Aachen Applied and Computational Mathematics

   RWTH Aachen University · Graphic Era University

   Affiliation as printed

   Applied and Computational Mathematics, RWTH Aachen University, Germany

   Department of Mathematics, Graphic Era Deemed to be University, Dehradun, Uttarakhand, India