Least-squares spectral element solution of incompressible Navier-Stokes equations with adaptive refinement

Ozcelikkale, Altug
Sert, Cüneyt
Least-squares spectral element solution of steady, two-dimensional, incompressible flows are obtained by approximating velocity, pressure and vorticity variable set on GaussLobatto-Legendre nodes. Constrained Approximation Method is used for h- and p-type nonconforming interfaces of quadrilateral elements. Adaptive solutions are obtained using a posteriori error estimates based on least squares functional and spectral coefficient. Effective use of p-refinement to overcome poor mass conservation drawback of leastsquares formulation and successful use of h- and p-refinement together to solve problems with geometric singularities are demonstrated. Capabilities and limitations of the developed code are presented using Kovasznay flow, flow past a circular cylinder in a channel and backward facing step flow.


Least-squares finite element solution of Euler equations with adaptive mesh refinement
Akargün, Hayri Yiğit; Sert, Cüneyt; Department of Mechanical Engineering (2012)
Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the me...
Least-squares finite element solution of Euler equations with H-type mesh refinement and coarsening on triangular elements
AKARGUN, Hayri Yigit; Sert, Cüneyt (2014-01-01)
Purpose - The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows.
Numerical solution of magnetohydrodynamic flow problems using the boundary element method
Tezer, Münevver (2005-03-18)
A boundary element solution is given for a magnetohydrodynamic (MHD) flow problem in a rectangular duct having insulating walls, in terms of velocity and induced magnetic field. The coupled velocity and magnetic field equations are first transformed into decoupled nonhomogeneous convection-diffusion type equations and then finding particular solutions, the homogeneous equations are solved using the boundary element method (BEM). The fundamental solutions of the decoupled homogeneous equations themselves are...
YAVUZ, H; BUYUKDURA, OM (1994-04-14)
A rigorous integral equation formulation for the analysis of a phased array of flangemounted waveguide apertures is given for a finite number of elements and nonuniform spacings. The resulting set of ihtegrd equations is reduced to a matrix equation called the coupling matrix which relates the coefficients of all the modes in all the waveguides to one another. The solution then yields the dominant mode reflection coefficient, coefficients of scattered modes and hence the field in each waveguide. The blockTo...
Dual reciprocity boundary element method for magnetohydrodynamic flow using radial basis functions
Tezer, Münevver (2002-02-01)
A dual reciprocity boundary element method is given to obtain the solution in terms of velocity and induced magnetic field for the study of MHD (magnetohydrodynamic) flow through a rectangular duct having insulating walls. The equations are transformed to two types of nonlinear Poisson equations and the right-hand sides in these equations are approximated using combinations of two classes of radial basis functions (the value of the function and its normal derivatives are utilized for approximation). Computa...
Citation Formats
A. Ozcelikkale and C. Sert, “Least-squares spectral element solution of incompressible Navier-Stokes equations with adaptive refinement,” JOURNAL OF COMPUTATIONAL PHYSICS, pp. 3755–3769, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46272.