Abstract
In this paper, we present numerical results obtained by an in-house incompressible fluid flow solver based on isogeometric analysis (IgA) for the standard benchmark problem for incompressible fluid flow simulation – lid-driven cavity flow. The steady Navier-Stokes equations are solved in their velocity-pressure formulation and we consider only inf-sup stable pairs of B-spline discretization spaces. The main aim of the paper is to compare the results from our IgA-based flow solver with the results obtained by a standard package based on finite element method with respect to degrees of freedom and stability of the solution. Further, the effectiveness of the recently introduced rIgA method for the steady Navier-Stokes equations is studied.The authors dedicate the paper to Professor K. Kozel on the occasion of his 80th birthday.
Highlights
The fluid flow simulation is one of the fundamental problems solved in engineering practice
We present the numerical results obtained by our in-house isogeometric fluid flow solver for the model problem, lid-driven cavity flow, and compare them with reference solutions and with the numerical results obtained by standard package FEniCS, which is based on the finite element method
On more complicated domains, where finite element meshes only approximate the domain boundary, isogeometric analysis have an advantage of exact representation of the computational domain by a B-spline/Non-Uniform Rational B-spline (NURBS) mesh
Summary
The fluid flow simulation is one of the fundamental problems solved in engineering practice. Recently, Hughes et al (see [4, 5]) introduced a powerful numerical method for solving partial differential equations called isogeometric analysis (IgA). This method has many features common with FEM and the main motivation is to bridge the gap between geometric modelling (Computer-Aided Design – CAD) and numerical simulation (Finite Element Analysis – FEA). One would like to use directly the description of an object in CAD system for numerical simulations This is not possible with the standard approaches (FDM, FVM, FEM) since they require the construction of some computational mesh (typically, triangular/quadrilateral meshes for 2D problems and tetrahedral/hexahedral for 3D problems) which is, only an approximation of the original computational domain
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