The design and analysis of numerical methods are usually guided by the following:(a) von
Neumann analysis using Fourier series expansion of unknowns,(b) the modified differential …

Numerical investigation of a compressible fluid in a two-dimensional rectangular lid-driven
cavity (LDC) with a vertical temperature gradient is performed by solving the compressible …

The study presents a comprehensive numerical investigation of the Kelvin–Helmholtz
Rayleigh–Taylor Instability (KHRTI) onset using highly resolved peta-scale direct numerical …

Rayleigh-Taylor instability (RTI) occurs at the interface of two media when the heavier fluid is
accelerated into the lighter fluid and is a prototypical hydrodynamic event present in many …

Three-dimensional direct numerical simulations (DNS) of Rayleigh-Taylor instability (RTI) at
the interface of two masses of air with a sharp temperature gradient of 149 K are performed …

We present a new spectral framework to design and optimise numerical methods for
convection problems termed Local Transfer function Analysis (LTA), which improves the …

An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-
dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as …

This paper presents a newly developed higher order compact scheme that is designed on a
polar grid by using an implicit form of first order derivatives on nonuniform grids. These …

In this work, the Global Spectral Analysis (GSA) is applied to the convective Lax–Wendroff
based discretization of linear convection–diffusion problem in both 1D and 2D. Contrary to …

In this work, we revisit and propose some improvements in the combined spatial-temporal
approximate dispersion analysis (ADR). This analysis serves the purpose of quantifying …