摘要:

AbstractThis paper presents ap‐ version least squares finite element formulation (LSFEF) for two‐dimensional, incompressible, non‐Newtonian fluid flow under isothermal and non‐isothermal conditions. The dimensionless forms of the diffential equations describing the fluid motion and heat transfer are cast into a set of first‐order differential equations using non‐Newtonian stresses and heat fluxes as auxiliary variables. The velocities, pressure and temperature as well as the stresses and heat fluxes are interpolated using equal‐order,C0‐continuous,p‐version hierarchical approximation functions. The application of least squares minimization to the set of coupled first‐order non‐linear partial differential equations results in finding a solution vector {δ} which makes the partial derivatives of the error functional with respect to {δ} a null vector. This is accomplished by using Newton's method with a line search.The paper presents the implementation of a power‐law model for the non‐Newtonian Viscosity. For the non‐isothermal case the fluid properties are considered to be a function of temperature. Three numerical examples (fully developed flow between parallel plates, symmetric sudden expansion and lid‐driven cavity) are presented for isothermal power‐law fluid flow. The Couette shear flow problem and the 4:1 symmetric sudden expansion are used to present numerical results for non‐isothermal power‐law fluid flow. The numerical examples demonstrate the convergence characteri

ISSN:0271-2091    

DOI:10.1002/fld.1650180202

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractA single‐point model in the vertical is used to examine the coupling between tidal currents and wind‐driven flows in shallow near‐coastal regions. Calculations using both a linear slip and a no‐slip condition at the sea bed clearly show that coupling between tidal and wind‐driven currents cannot occur in a linear model with a time‐independent eddy viscosity. However with a physically more realistic time‐varying viscosity related to the flow field, coupling does occur, the magnitude of this non‐linear interaction depending upon the change in eddy viscosity over a tidal cycle and the intensity of shear in the vertical. A point model in the vertical with flow induced by an oscillatory pressure gradient and an additional constant wind stress is used to examine the influence of viscosity parametrization and water depth upon this coupling.The solution in the vertical is accomplished using both a functional approach and a finite difference method. Some conclusions as to the relative merits of these approaches, particularly the use of a transformed grid in the case of high‐shear surface and bed boundary layers, are

ISSN:0271-2091    

DOI:10.1002/fld.1650180203

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractA finite element (FE) analysis of experimentally observed creeping thermal plumes in a medium whose viscosity is strongly temperature‐dependent is performed. Such plumes are considered to play an important role in numerous geological processes and numerical modelling is often the only option to study their physics. Initial simulations by means of the general‐purpose Galerkin finite element package NACHOS‐II demonstrated serious deficiencies of the method in modelling plumes with large viscosity contrasts, in spite of several options for the solution (mixed or penalty formulation) and the elements (continuous or discontinous pressure). In agreement with observations from FE simulations of isothermal Stokes flow in other studies, we have isolated the violation of the div = 0 or incompressibility constraint as the major culprit in the failure of the FE method. It is demonstrated that thea posterioricomputed discrete divergence (DDIV) can be used as a diagnostic tool to evaluate the reliability of the FE solution and to rank the solution and element options provided in the NACHOS code. On the basis of these considerations, the combination of the mixed method with aQ2‐P1(discontinuous pressure) element turns out to be the most suitable for the present plume problem but is still unable to sufficiently enforce the div = 0 condition. With a goal to remedy this detrimental behaviour, several FE modifications and new approaches have been taken. These include: (i) use of a new scaling option for the governing equations which has the effect of equilbrating the stiffness matrices and thus improving their condition; (ii) implementation of several iterative solution techniques such as the iterated penalty and the Uzawa algorithm for the augmented Langrangian to better accommodate the dual role of the pressure; (iii) use of a multistep Newton method to better handle the high non‐linearity of the coupled flow/transport problem. Although each of these options (or a combination of them) is able to improve on the quality of FE solution, the most startling amelioration has been gained with option (iii). Use of the latter resulted in very satisfactory modelling of the experimentally observ

ISSN:0271-2091    

DOI:10.1002/fld.1650180204

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper deals with a critical evaluation of various finite element models for low‐viscosity laminar incompressible flow in geometrically complex domains. These models use Galerkin weighted residuals UVP, continuous penalty, discrete penalty and least‐squares procedures. The model evaluations are based on the use of appropriate tensor product Lagrange and simplex quadratic triangular elements and a newly developed isoparametric Hermite element. All of the described models produce very accurate results for horizontal flows. In vertical flow domains, however, two different cases can be recognized. Downward flows, i.e. when the gravitational force is in the direction of the flow, usually do not present any special problem. In contrast, laminar flow of low‐viscosity Newtonian fluids where the gravitational force is acting in the direction opposite to the flow presents a difficult case. We show that only by using the least‐squares method in conjunction withC1‐continuous Hermite elements can this type of laminar flow be modelled accurately. The problem of smooth isoparametric mapping ofC1Hermite elements, which is necessary in dealing with geometrically complicated domains, is tackled by means of an auxiliary optimization procedure. We conclude that the least‐squares method in combination with isoparmetric Hermite elements offers a new general‐purpose modelling technique which can accurately simulate all types of low‐viscosity incompressible laminar flow in

ISSN:0271-2091    

DOI:10.1002/fld.1650180205

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650180206

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650180201

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY