Finite analytic numerical method for unsteady two-dimensional Navier-Stokes equations

The group finite element formulation

A simple mixed finite element method is developed to solve the steady state, incompressible Navier-Stokes equations in a neighborhood of an isolated--but not necessarily unique--solution Convergence is established under very mild restrictions on the triangulation, and, when the solution is sufficiently smooth, optimal error bounds are obtained

An analysis of a mixed finite element method for the Navier-Stokes equations

Spectral-element methods, based on high-order polynomials, are among the most commonly used techniques for computing accurate simulations of wave propagation phenomena in complex media. However, to retain computational efficiency, very high order polynomials cannot be used and errors such as numerical dispersion and numerical anisotropy cannot be totally avoided. In the present work, we devise an approach for reducing such errors by considering modified discrete wave operators. We analyze consistent and lumped operators together with blended operators (weighted averages of consistent and lumped operators). Furthermore, using the operator-blending approach and a novel dispersion analysis method, we develop optimal spectral-element operators that have increased numerical accuracy, without resorting to very high order operators. The new operators are faster and computationally more efficient than consistent operators. Our approach is based on the tensor product decomposition of the element matrices into 1D f...

Optimal blended spectral-element operators for acoustic wave modeling

SUMMARY The results of a numerical study of the viscous oscillating flow around a circular cylinder at low Keulegan‐ Carpenter numbers (KC) and frequency parameters (b) are presented in this paper. The finite element method was used for the solution of the Navier‐Stokes equations in the formulation where the streamfunction and vorticity are the field variables. The computation was conducted at Keulegan‐Carpenter numbers extending up to KCa 15 and frequency parameters ranging between ba 6 and 100. At low values of the Keulegan‐Carpenter number the flow remains symmetrical. As the Keulegan‐Carpenter number is increased over a certain value which depends also on the frequency parameter, asymmetries appear in the flow which are eventually amplified and lead finally to complex vortex-shedding patterns, some of which are markedly different from those observed at higher frequency parameters. The solution revealed that although for certain values of KC and b the shedding of vortices is periodic, there also exists a complicated flow regime in which the flow is not periodic but switches between different modes in consecutive cycles of flow oscillation. For the various flow cases examined, the traces of the hydrodynamic forces are presented and the hydrodynamic coefficients and RMS values of the inline force are compared with experimental evidence. # 1998 John Wiley & Sons, Ltd.

C.A. Brebbia

Papers

Finite-element solution of navier-stokes equations for transient two-dimensional incompressible flow