This paper compares LES results of a cylinder flow with two sets of numerical schemes, two span lengths, and a coarse and refined mesh. One set of the numerical scheme is the 7th order WENO scheme for the inviscid fluxes and 6th order central differencing for the viscous terms (7-6), the other set is a 5th order WENO scheme with a 4th order central differencing(5-4). For this purpose, a fully c...

In this paper, we propose a high order residual distribution conservative finite difference scheme for solving convection– diffusion equations on non-smooth Cartesian meshes. WENO (weighted essentially non-oscillatory) integration and linear interpolation for the derivatives are used to compute the numerical fluxes based on the point values of the solution. The objective is to obtain a high ord...

In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state hyperbolic conservation laws on non-smooth Cartesian or other structured curvilinear meshes. WENO (weighted essentially non-oscillatory) integration is used to compute the numerical fluxes based on the point values of the solution, and the principles of residual distributi...

Implicit variant WENO schemes with anti-diffusive flux for compressible flow computations are presented. These variant WENO schemes include the antis for the preconditioned compressible Euler/Navier-Stokes equations are also considered. The numerical flux of the variant WENO scdiffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator. Implicit WENO schemeheme is cons...

Runge Kutta Discontinuous Galerkin (RKDG) schemes can provide highly accurate solutions for a large class of important scientific problems. Using them for problems with shocks and other discontinuities requires that one has a strategy for detecting the presence of these discontinuities. Strategies that are based on total variation diminishing (TVD) limiters can be problem-independent and scale-...

This paper is devoted to comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is ut þ ðu uÞx 1⁄4 ðuuxxxÞx, which arises in the context of thin film flow. First we employ implicit schemes and treat both convection and diffusion terms implicitly. Then the convection terms are treated with wellknown explicit schemes, namely Godunov,...

We develop an alternative formulation of conservative finite difference weighted essentially non-oscillatory (WENO) schemes to solve conservation laws. In this formulation, the WENO interpolation of the solution and its derivatives are used to directly construct the numerical flux, instead of the usual practice of reconstructing the flux functions. Even though this formulation is more expensive...

Stratocumulus clouds are the most common type of boundary layer cloud; their radiative effects strongly modulate climate. Large eddy simulations (LES) of stratocumulus clouds often struggle to maintain fidelity to observations because of the sharp gradients occurring at the entrainment interfacial layer at the cloud top. The challenge posed to LES by stratocumulus clouds is evident in the wide ...

This thesis is concerned with effective and robust numerical schemes for solving steady Euler equations. For solving the nonlinear system resulting from the discretization of the steady Euler equations, we employ a standard Newton method as the outer iterative scheme and a linear multigrid method as the inner iterative scheme with the block lower-upper symmetric Gauss-Seidel iteration as its sm...