Quantifying parameter ranges for high fidelity simulations for prescribed accuracy by Lax–Wendroff method

Abstract

Explicit second order central difference (CD2) based Lax–Wendroff (LW) method is evaluated for large eddy simulation here, using global spectral analysis (GSA) for its ability to compute fluid flows up to a specified accuracy. While the LW method has been analyzed for numerical stability in the past, rigorous quantification for performing accurate simulations including error dynamics has not been reported before. This is addressed here by determining optimal numerical parameters for prescribed accuracies based on the GSA of 2D convection–diffusion equation (CDE), which is the main focus of the present research. First, two LW methods are reported based on the application of the method for convection and both convection and diffusion operators, respectively, with the latter also having third derivative dispersive and fourth order diffusion terms. Using GSA, the optimal scheme is determined by comparing the two schemes for accuracy. The accuracy of GSA for wave propagation is also demonstrated by the validation of the q-waves determined from the analysis with the numerical simulations of 2D CDE. Finally, 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., 2020)”, optimal simulation parameters are determined for the accuracy in representing physical diffusion of the scheme and validated using simulations of the canonical lid-driven cavity problem for a sub- and a super-critical Reynolds number.