A characteristic/finite element algorithm for the 3-D Navier-Stokes equations using unstructured grids
type: Item
instance of: scholarly article
title: A characteristic/finite element algorithm for the 3-D Navier-Stokes equations using unstructured grids
zbMATH Open document ID: 0967.76057
DOI: 10.1016/S0045-7825(99)00003-1
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2001-08-30T00:00:00Z
review text: This paper discusses a finite element algorithm for solution of three-dimensional Navier-Stokes equations that is based on the method of characteristics. The algorithm which employs a time-slitting of convective terms form the generalized Stokes problem, comprises a point-wise characteristic integration of convective terms, and Uzawa integration of the generalized Stokes problem. The most costly part of the characteristic integration scheme is the search for an element containing the foot of a given characteristic. The present study uses a very efficient algorithm for element searching, which is particularly useful for complex geometries. We discuss the implementation of the algorithm, and compare the resulting code's performance with that of a code based on a more conventional, fourth-order Runge-Kutta convection integration. A variety of flow problems are tested, including an analytical solution of the Navier-Stokes equations, flow in a lid-driven cavity flow, flow over a backward-facing step, and flow in an end-to-side anastomosis. In all cases, the proposed algorithm demonstrates peformance superior to that of a conventional explicit treatment of convective terms.
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65M25
zbMATH DE Number: 1442926
zbMATH Keywords: flow in end-to-side anastomosis
zbMATH Keywords: flow over backward-facing step
zbMATH Keywords: finite element algorithm
zbMATH Keywords: three-dimensional Navier-Stokes equations
zbMATH Keywords: method of characteristics
zbMATH Keywords: time-slitting of convective terms
zbMATH Keywords: generalized Stokes problem
zbMATH Keywords: point-wise characteristic integration
zbMATH Keywords: Uzawa integration
zbMATH Keywords: element searching
zbMATH Keywords: lid-driven cavity flow
author: P. D. Minev
author: C. Ross Ethier
MaRDI profile type: Publication
cites work: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
cites work: The method of weighted residuals and variational principles. With application in fluid mechanics, heat and mass transfer
cites work: On the transport-diffusion algorithm and its applications to the Navier-Stokes equations
cites work: Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics
cites work: Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations
cites work: Numerical method for unsteady viscous hydrodynamical problem with free boundaries
cites work: A high-order characteristics/finite element method for the incompressible Navier-Stokes equations
cites work: A comparison of integration and interpolation Eulerian‐Lagrangian methods
cites work: An operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow
cites work: Q3817902
cites work: Some fast 3D finite element solvers for the generalized Stokes problem
cites work: Implementation of the Lagrange‐Galerkin method for the incompressible Navier‐Stokes equations
cites work: Exact fully 3D Navier–Stokes solutions for benchmarking
cites work: Application of a fractional-step method to incompressible Navier-Stokes equations
cites work: AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE FLOW USING SPECTRAL ELEMENTS
full work available at URL: s0045-7825(99)00003-1
OpenAlex ID: W2079250961
description: scientific article; zbMATH DE number 1442926