摘要:

AbstractThe numerical solution of the compressible Euler and Navier‐Stokes equations in primitive variables form requires the use of artificial viscosity or upwinding. Methods that are first‐order‐accurate are too dissipative and reduce the effective Reynolds number substantially unless a very fine grid is used. A first‐order finite element method for the solution of the Euler and Navier‐Stokes equations can be constructed by adding Laplacians of the primitive variables to the governing equations. Second‐order schemes may require a fourth‐order dissipation and higher‐order elements. A finite element approach is proposed in which the fourth‐order dissipation is recast as the difference of two Laplacian operators, allowing the use of bilinear elements. The Laplacians of the primitive variables of the first‐order scheme are thus balanced by additional terms obtained from the governing equations themselves, tensor identities or other forms of nodal averaging. To demonstrate formally the accuracy of this scheme, an exact solution is introduced which satisfies the continuity equation identically and the momentum equations through forcing functions. The solutions of several transonic and supersonic inviscid and laminar viscous test cases are also presented and compared to other avail

ISSN:0271-2091    

DOI:10.1002/fld.1650200802

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractIn this article we discuss the fictitious domain solution of the Navier‐Stokes equations modelling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary conditions to be satisfied and is particularly well suited to the treatment of no‐slip boundary conditions. This approach allows the use of structured meshes and fast specialized solvers for problems on complicated geometries. Another interesting feature of the fictitious domain approach is that it allows the solution of optimal shape problems without regriding. The resulting methodology is applied to the solution of flow problems including external incompressible viscous flow modelled by the Navier‐Stokes equations and then to an optimal shape problem for Stokes and Navier‐Stok

ISSN:0271-2091    

DOI:10.1002/fld.1650200803

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA cell‐vertex finite volume formulation, using local finite element approximations to calculate fluxes through an auxiliary mesh (control volumes) is used to solve inviscid and viscous compressible flow equations on unstructured grids. Non‐linear artificial viscosity methods are adopted to avoid decoupling and capture shock waves. Artificial time‐dependent terms are augmented if needed, to guarantee convergence of common iterative procedures to a steady‐state solution. The incompressible limit of compressible flow equations is studied. A unified approach for solving both compressible and incompressible flow problems is proposed. Also some results of a zonal formulation with different governing equations in different regions are presented. Applications to the solution of Maxwell's equations for wave propagation and scattering are discussed in an a

ISSN:0271-2091    

DOI:10.1002/fld.1650200804

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA unified theory of non‐oscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This leads to symmetric and upstream limited positive (SLIP and USLIP) schemes which can be formulated on either structured or unstructured meshes. The second part examines the application of similar ideas to the treatment of systems of conservation laws. An analysis of discrete shock structure leads to conditions on the numerical flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a convective upwind and split pressure (CUSP) scheme, in which the coefficient of the pressure differences is fully determined by the coefficient of convective diffusion. Numerical results are presented which confirm the properties of these scheme

ISSN:0271-2091    

DOI:10.1002/fld.1650200805

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractWe give an overview of some recent results concerning quantitative adaptive error control in CFD.

ISSN:0271-2091    

DOI:10.1002/fld.1650200806

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractTo avoid the use of pesticides on putting greens of golf courses, a temperature regulator system is strongly recommended nowadays in Japan. To maintain grass on the putting green without pesticide, the temperature of the ground should be controlled. This system consists of a cooling machine and buried pipes in the ground. The temperature of the water in the pipes cannot be regulated. In this paper, both identification and control problems are presented by the minimization technique and applied to a practical problem. To establish the system, it is important to obtain accurate parameters which are included in the governing equation. These parameters can be determined by parameter identification. The conjugate gradient method is used for the parameter identification procedure. The control problem aims to make the temperature at arbitrary points close to the objective temperature. The discrete‐time dynamic programming is used for the control procedur

ISSN:0271-2091    

DOI:10.1002/fld.1650200807

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractAn unstructured finite element method is presented for calculation of turbulent flow fields about aerospace configurations. Algebraic, one‐equation, and two‐equation turbulence models are implemented and compared. A new procedure for implementing an unstructured algebraic model without an auxiliary structured grid is presented. The overall procedure is applied to simulation of flow about launch vehicle configurations. The turbulence models are evaluated for calculation of flow fields about a forebody with shock induced separation. For this case. the one‐equation model gives better predictions. An inviscid flow field about a complete launch vehicle with multiple boosters is also evaluated to demonstrate the overall proc

ISSN:0271-2091    

DOI:10.1002/fld.1650200808

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractTurbulence modelling is done traditionally in fluid mechanics departments. However, mathematical tools such as frame invariance, multiple scale expansions and the like are of great help.We shall demonstrate these facts by applying mathematical and numerical tools to theK–εmodel. We shall investigate wall laws. Reynolds hypothesis, positivity ofkand ε and flows with multiple scales.We shall also take this opportunity to review some mathematical results relevant to turbulence modell

ISSN:0271-2091    

DOI:10.1002/fld.1650200809

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractRecently, a rigorousa posteriorierror estimate, based on the element residual method, for the steady‐state Navier‐Stokes equations has been derived. In this paper, by using this error estimate, we construct anhpadaptive strategy to minimize the total computation costs while achieving a targeted accuracy for steady incompressible viscous flow problems. The basichpadaptive strategy is to solve the approximate problem in three consecutive stages corresponding to three different meshes, i.e. an initial mesh, an intermediate adaptiveh‐mesh, and a final adaptivehpmesh. Our numerical result shows that the three‐stephpadaptive strategy for the incompressible flow problems indeed provides an accurate approximate solution while keeping the computational costs under

ISSN:0271-2091    

DOI:10.1002/fld.1650200810

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThis paper discusses the different sources of non‐physical entropy production which occur in the numerical resolution of the Euler equations for compressible inviscid flow and proposes several ways of correcting these effects. In particular a hybrid corrected centred, augmented by an accurate upwind scheme near singular boundaries is proposed which satisfies the mathematical entropy condition, and which solves the flow accurately within regions near non‐smooth boundaries of the computational domain. A coupled new dynamic auto‐adaptive mesh algorithm which produces highly accurate solutions is also introduced. This algorithm is non‐hierarchical. i.e. it does not depend on a fixed background mesh, which allows structural and geometrical changes and generates extremely precise discretizations for steady and unstea

ISSN:0271-2091    

DOI:10.1002/fld.1650200811

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY