Research Projects

The Boltzmann equation is a seven-dimensional equation, with moments of the Boltzmann equation reducing its dimensionality. The Euler equations are a five-moment hyperbolic model obtained under local thermodynamics equilibrium, ignoring collisions and viscous terms. Plasma flows are typically modeled by magnetohydrodynamics (MHD) equations, which assume quasi-neutrality of the plasma. A more generalized plasma flow model is considered, where electrons and ions in ideal plasma flows are unbounded, creating an electric and magnetic field. The Two-Fluid Euler equations is an example of a plasma flows model, a coupled system of Euler equations of ions, electrons, and Maxwell's equations by the stiff source term. When local thermodynamics equilibrium assumption fails, Ten-Moment equations are generated, resulting in the Two-fluid Ten-Moment plasma model. Relativistic hydrodynamics equations are used to model astrophysical flows when the fluid moves at speeds comparable to the speed of light. Several numerical strategies have been used to develop numerical schemes for governed systems, but they often face stability issues due to stiffness in flux and source. This work proposes designing finite difference WENO schemes for Two-fluid plasma models, which are robust, efficient, and high-order accurate. The approach combines positivity preserving limiters in WENO reconstruction and an integrating factor-based Runge Kutta approach to treat the source term. The work considers the Two-Fluid Euler plasma equations, Two-Fluid Ten-Moment plasma equations, and Two-Fluid relativistic plasma flow equations. A hybrid reconstruction approach is also designed to obtain efficient high-order schemes for the models.