A computational methodology for two‐dimensional fluid flows

Abstract

SUMMARYA weighted residual collocation methodology for simulating two‐dimensional shear‐driven and natural convection flows has been presented. Using a dyadic mesh refinement, the methodology generates a basis and a multiresolution scheme to approximate a fluid flow. To extend the benefits of the dyadic mesh refinement approach to the field of computational fluid dynamics, this article has studied an iterative interpolation scheme for the construction and differentiation of a basis function in a two‐dimensional mesh that is a finite collection of rectangular elements. We have verified that, on a given mesh, the discretization error is controlled by the order of the basis function. The potential of this novel technique has been demonstrated with some representative examples of the Poisson equation. We have also verified the technique with a dynamical core of a two‐dimensional flow in primitive variables. An excellent result has been observed—on resolving a shear layer and on the conservation of the potential and the kinetic energies—with respect to previously reported benchmark simulations. In particular, the shear‐driven simulation at CFL = 2.5 (Courant–Friedrichs–Lewy) and scriptRe MathClass-rel= 1000 (Reynolds number) exhibits a linear speed up of CPU time with an increase of the time step, Δt. For the natural convection flow, the conversion of the potential energy to the kinetic energy and the conservation of total energy is resolved by the proposed method. The computed streamlines and the velocity fields have been demonstrated. Copyright © 2014 John Wiley & Sons, Ltd.

Experimental and Numerical Investigation of a Novel Technique for Perforation in Petroleum Reservoir

“…This algorithm is based on the interpolation scaling function and the wavelet interpolation transform. This computational methodology has also been verified for several other applications such as heat and mass transfer, shear-driven and natural convection flows which can be found in Alam et al (2012Alam et al ( , 2014. The main objective of the present article is to focus on the simulation results for the flow in well reservoirs under in situ condition, rather than the contribution toward the development of the numerical scheme.…”

“…For non-Commercial computational algorithm, we use a computational methodology based on weighted residual collocation method (Finlayson, 1972) developed by Alam et al (2014). This algorithm is based on the interpolation scaling function and the wavelet interpolation transform.…”

Fujiwhara interaction of tropical cyclone scale vortices using a weighted residual collocation method

“…Using the DD subdivision method [20], the procedure for computing ' 0 j . / is given in detail by [23]. / is given in detail by [23].…”

“…Similarly, a further dilation by a factor of 1=2 leads to ' k .x/ that is shown in Figure 1(d). For convenience, we describe the following properties by restricting ' k .x/ on the x-axis [20,23]. For convenience, we describe the following properties by restricting ' k .x/ on the x-axis [20,23].…”

“…We have studied a multiresolution approximation (MRA) method (e.g. In contrast, it is a novel multiscale modeling idea being developed [21][22][23], is not fully understood, and the necessary ingredients behind the model stand on some powerful computational methods. Second, the subdivision scheme of [20] (Deslauriers-Dubuc (DD) subdivision) is investigated toward the development of a weighted residual collocation methodology [14] for solving the equations.…”