Numerical solutions of incompressible Euler and Navier-Stokes equations by efficient discrete singular convolution method

Abstract

An efficient discrete singular convolution (DSC) method is introduced to the numerical solutions of incompressible Euler and Navier-Stokes equations with periodic boundary conditions. Two numerical tests of two-dimensional NavierStokes equations with periodic boundary conditions and Euler equations for doubly periodic shear layer flows are carried out by using the DSC method for spatial derivatives and fourth-order Runge-Kutta method for time advancement, respectively. The computational results show that the DSC method is efficient and robust for solving the problems of incompressible flows, and has tile potential of being extended to numerically solve much broader problems in fluid dynamics.

Discrete Singular Convolution–Finite Subdomain Method for the Solution of Incompressible Viscous Flows

“…The details of the discretized expressions for the FTSPFM and elaborate details of the numerical solution procedure are available in Refs. [32,33].…”

Fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method

“…Since then, applications of DSC method to various science and engineering problems have been investigated and their successes have demonstrated the potential of this method as an attractive numerical analysis technique [16][17][18][19][20][21]. As stated by Wei [22][23][24] singular convolutions (SC) are a special class of mathematical transformations, which appear in many science and engineering problems, such as the Hilbert, Abel, and Radon transforms.…”

“…The DSC algorithm can be realized by using many approximation kernels. However, it was shown [17][18][19][20][21][22][23][24][25][26][27][28] that for many problems, the use of the regularized Shannon kernel (RSK) is very efficient. The RSK is given by [26]:…”

Discrete singular convolution methodology for free vibration and stability analyses of arbitrary straight‐sided quadrilateral plates

“…It is also known that the truncation error is very small due to the use of the Gaussian regularizer; the above formulation given by Equation (4) is practical and has an essentially compact support for numerical interpolation. Equation (4) can also be used to provide discrete approximations to the singular convolution kernels of the delta type [60,61] …”