  The analysis of Lax-Wendroff (LW) method is performed by the generic modified
differential equation (MDE) approach in the spectral plane using Fourier
transform. In this approach, the concept of dispersion relation plays a major
role relating spatial and temporal dependence of the governing differential
equation, including initial and boundary conditions in developing high accuracy
schemes. Such dispersion relation preserving schemes are calibrated in the
spectral plane using the global spectral analysis for the numerical method in
the full domain. In this framework, the numerical methods are calibrated by
studying convection and diffusion as the underlying physical processes for this
canonical model problem. In the LW method spatial and temporal discretizations
are considered together, with time derivatives replaced by corresponding
spatial derivatives using the governing equation. Here the LW method is studied
for the convection-diffusion equation (CDE) to establish limits for numerical
parameters for an explicit central difference scheme that invokes third and
fourth spatial derivatives in the MDE, in its general form. Thus, for the LW
method, two different MDEs are obtained, depending on whether the LW method is
applied only on the convection operator, or both on the convection and
diffusion operators. Motivated by a one-to-one correspondence of the
Navier-Stokes equation with the linear CDE established in "Effects of numerical
anti-diffusion in closed unsteady flows governed by two-dimensional
Navier-Stokes equation- Suman et al. Comput. Fluids, 201, 104479 (2020)", an
assessment is made here to solve flow problems by these two variants of the LW
method. Apart from mapping the numerical properties for performing large eddy
simulation for the LW methods, simulations of the canonical lid-driven cavity
problem are performed for a super-critical Reynolds number for a uniform grid.

Fluid Dynamics;Numerical Analysis;Numerical Analysis