Numerical investigation of thermal non-equilibrium effects of diatomic and polyatomic gases on the shock-accelerated square light bubble using a mixed-type modal discontinuous Galerkin method

Spatiotemporal pattern formation in nonlinear coupled reaction-diffusion systems with a mixed-type modal discontinuous Galerkin approach

“…We present here a mixed-type modal discontinuous Galerkin (DG) formulation to solve the one and two-dimensional NCRD systems (1), which has been proven to be an appropriate technique for dealing with second-order derivatives in diffusion terms [46,50,51]. A new variable, Θ, is introduced in this formulation, which can be thought of as the derivatives of unknown variables.…”

“…Over past years, Cockburn and co-authors devised a framework for solving PDEs based hyperbolic conservation laws in a series of works [36,37,38,39,40,41,42,42] that contributed significantly to the development of the DG technique. This method has been effectively implemented to several problems, including fluid flows, multi-phase flows, quantum physics, magnetohydrodynamics, and many others [43,44,45,46,47,48,49,50,51], it has just recently made its way into developmental biology. This implementation is motivated by advancements in the approach as well as recent breakthroughs in spatiotemporal pattern generation, which have made the DG method a viable instrument for a broader range of biological and chemical requisitions.…”

Contribution of Mach number to the evolution of the Richtmyer-Meshkov instability induced by a shock-accelerated square light bubble

“…These methods are locally conservative, stable, and high-order accurate methods which can easily handle complex geometries, irregular meshes with hanging nodes, and approximations that have polynomials of different degrees in different elements. In this paper, the two-dimensional compressible Navier-Stokes-Fourier equations ( 1) are solved by an in-house developed explicit mixed-type modal DG solver based on structured meshes [37,38,57,62]. The computational domain is discretized into rectangular elements, and scaled Legendre polynomial functions are employed for the elements.…”

“…Singh [37] investigated numerically the impacts of the Atwood numbers on the flow evolution of a shock-accelerated square bubble containing various gases at low Mach number (M s = 1.22) and observed that the Atwood number has a significant impact on the flow evolution with complex wave pattern, vortex creation, vorticity generation, and bubble deformation. Recently, Singh [38] explored numerically the thermal nonequilibrium effects of diatomic and polyatomic gases on the flow dynamics of a shock-accelerated square light bubble.…”

Computational Modeling of Nonlinear Reaction-Diffusion Fisher–KPP Equation with Mixed Modal Discontinuous Galerkin Scheme

“…The DG approaches integrate the advantages of modern CFD methods, including Finite Element (FE) and Finite Volume (FV) methods, and have been effectively utilized to a broad spectrum of scientific problems, including computational fluid dynamics, plasma physics, quantum physics, biological sciences, and many others. (Le et al 2014;Raj et al, 2017;Singh and Myong, 2017;Singh, 2018;Chourushi et al, 2020;Singh, 2021a;Singh, 2021b;Singh, 2021c). The DG approaches have several key characteristics that make them interesting for usage in applications.…”