journal article
LitStream Collection
Home
Kovacs, Agnes; Kawahara, Mutsuto
doi: 10.1002/fld.1650130402pmid: N/A
In this paper a finite element solution for two‐dimensional incompressible viscous flow is considered. The velocity correction method (explicit forward Euler) is applied for time integration. Discretization in space is carried out by the Galerkin weighted residual method. The solution is in terms of primitive variables, which are approximated by piecewise bilinear basis functions defined on isoparametric rectangular elements. The second step of the obtained algorithm is the solution of the Poisson equation derived for pressure. Emphasis is placed on the prescription of the proper boundary conditions for pressure in order to achieve the correct solution. The scheme is completed by the introduction of the balancing tensor viscosity; this makes this method stable (for the advection‐dominated case) and permits us to employ a larger time increment. Two types of example are presented in order to demonstrate the performance of the developed scheme. In the first case all normal velocity components on the boundary are specified (e.g. lid‐driven cavity flow). In the second type of example the normal derivative of velocity is applied over a portion of the boundary (e.g. flow through sudden expansion). The application of the described method to non‐isothermal flows (forced convection) is also included.
doi: 10.1002/fld.1650130403pmid: N/A
The paper describes a method for solving numerically two‐dimensional or axisymmetric, and three‐dimensional turbulent internal flow problems. The method is based on an implicit upwinding relaxation scheme with an arbitrarily shaped conservative control volume. The compressible Reynolds‐averaged Navier‐Stokes equations are solved with a two‐equation turbulence model. All these equations are expressed by using a non‐orthogonal curvilinear co‐ordinate system. The method is applied to study the compressible internal flow in modern power installations. It has been observed that predictions for two‐dimensional and three‐dimensional channels show very good agreement with experimental results.
doi: 10.1002/fld.1650130404pmid: N/A
A marching finite volume method is presented for the calculation of two‐dimensional, subcritical and supercritical, steady open channel flow including the usually neglected terms of slope and bottom friction. The channel flow will be assumed to be homogeneous, incompressible, two‐dimensional and viscous with wind and Coriolis forces neglected. A hydrostatic pressure distribution is assumed throughout the flow field. The numerical technique used is a combination of the finite element and finite difference methods. A transformation is introduced through which quadrilaterals in the physical domain are mapped into squares in the computational domain. The governing system of PDEs is thus transformed into an equivalent system applied over a square grid network. Comparisons with other numerical solutions as well as with measurements for various open channel configurations show that the proposed approach is a comparatively accurate, reliable and fast technique.
Okamoto, Naotaka; Kawahara, Mutsuto
doi: 10.1002/fld.1650130405pmid: N/A
A numerical method is presented to analyse a steady convection‐diffusion problem with a first‐order chemical reaction defined on an infinite region. The present method is based on the combined finite element and boundary element methods. For one‐ and two‐dimensional examples in an infinite region the numerical results by the present method are in excellent agreement with the exact solutions. As a practical application, the simulation of the concentration distribution of the chemical oxygen demand at Kojima Bay is carried out.
Mehta, R. C.; Jayachandran, T.; Sastri, V. M. K.
doi: 10.1002/fld.1650130406pmid: N/A
A finite element algorithm for solving the Navier‐Stokes equations is presented for the analysis of high‐speed viscous flows. The algorithm uses triangular elements. The unsteady equations are integrated to steady state with a Runge‐Kutta time‐marching scheme. A postprocessing artificial dissipation term is introduced to stabilize the computations and to dampen dissipation errors. Numerical results are compared with the calculation of uniform flow on a rectangular region which encounters an embedded oblique shock. A shock/turbulent boundary layer problem is also solved and results are compared with experimental data. It is shown that the postprocessing smoothing term and boundary conditions similar to the finite difference method work well in the present numerical studies.
doi: 10.1002/fld.1650130407pmid: N/A
A numerical algorithm to determine the impingement of an axisymmetric free jet upon a curved deflector is presented. The problem is considered within the potential flow theory with the allowance of gravity and surface tension effects. The primary dependent variable is the Stokes streamfunction, which is approximated through finite elements using the isoparametric Hermite Zienkiewicz element. To find the correct position of the free boundaries, a trial‐and‐error method is employed which amounts to solving a boundary value problem (BVP) for the Stokes streamfunction at each iteration step. An efficient method is proposed to solve this BVP. The algorithm to find the correct position of the free boundaries is tested by computing the impingement upon an infinite disc and a hemispherical deflector. To confirm the correctness of the solution, each problem has been solved using several different mesh gradings. A comparison between the Zienkiewicz and the other standard C0 finite elements is also given.
doi: 10.1002/fld.1650130408pmid: N/A
A finite difference solution algorithm is described for use on two‐dimensional curvilinear meshes generated by the solution of the transformed Laplace equation. The efficiency of the algorithm is improved through the use of a full approximation scheme (FAS) multigrid algorithm using an extended pressure correction scheme as smoother. The multigrid algorithm is implemented as a fixed V‐cycle through the grid levels with a constant number of sweeps being performed at each grid level. The accuracy and efficiency of the numerical code are validated using comparisons of the flow over two backward step configurations. Results show close agreement with previous numerical predictions and experimental data. Using a standard Cartesian co‐ordinate flow solver, the multigrid efficiency obtainable in a rectangular system is shown to be reproducible in two‐dimensional body‐fitted curvilinear co‐ordinates. Comparisons with a standard one‐grid method show the multigrid method, on curvilinear meshes, to give reductions in CPU time of up to 93%.
doi: 10.1002/fld.1650130409pmid: N/A
In this paper we describe a time‐splitting method for the three‐dimensional shallow water equations. The stability of this method neither depends on the vertical diffusion term nor on the terms describing the propagation of the surface waves. The method consists of two stages and requires the solution of a sequence of linear systems. For the solution of these systems we apply a Jacobi‐type iteration method and a conjugate gradient iteration method. The performance of both methods is accelerated by a technique based on smoothing. The resulting method is mass‐conservative and efficient on vector and parallel computers. The accuracy, stability and computational efficiency of this method are demonstrated for wind‐induced problems in a rectangular basin.
Showing 1 to 10 of 10 Articles