On boundary conditions for the numerical solution of fluid dynamic problems

CALCOLO ◽  
1989 ◽  
Vol 26 (2-4) ◽  
pp. 149-165
Author(s):  
M. A. Pirozzi
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Fluid Dynamic ◽  
Dynamic Problems

Modelling solid transport in building drainage systems

1996 ◽  
Vol 33 (9) ◽  
pp. 9-16 ◽  
Author(s):  
John A. Swaffield ◽  
John A. McDougall
Keyword(s):  
Decision Making ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Water Conservation ◽  
Transient Flow ◽  
Drainage System ◽  
System Model ◽  
Flow Depth ◽  
Flow Conditions ◽  
Solid Transport

The transient flow conditions within a building drainage system may be simulated by the numerical solution of the defining equations of momentum and continuity, coupled to a knowledge of the boundary conditions representing either appliances discharging to the network or particular network terminations. While the fundamental mathematics has long been available, it is the availability of fast, affordable and accessible computing that has allowed the development of the simulations presented in this paper. A drainage system model for unsteady partially filled pipeflow will be presented in this paper. The model is capable of predicting flow depth and rate, and solid velocity, throughout a complex network. The ability of such models to assist in the decision making and design processes will be shown, particularly in such areas as appliance design and water conservation.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

scholarly journals Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 469 ◽  
Author(s):  
Azhar Iqbal ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spline Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
B Spline

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

Numerical Solution of a Hydrofoil Moving Near an Interface

1996 ◽  
Vol 40 (04) ◽  
pp. 269-277
Author(s):  
G. X. Wu ◽  
T. Miloh ◽  
G. Zilman
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Body Surface ◽  
Iteration Scheme ◽  
The Body ◽  
Two Fluids ◽  
Linearized Theory

The problem of a hydrofoil moving near an interface of two fluids of different densities is analyzed. An iteration scheme is proposed which imposes the boundary conditions on the body surface and on the interface alternately. The numerical solution is obtained by using the linearized theory and a Glauert-type expansion for the vortex distribution. Results are provided for various cases with different densities and different speeds.

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

scholarly journals Multi-Fidelity Simulation of a Turbofan Engine With Results Zoomed Into Mini-Maps for a Zero-D Cycle Simulation

2004 ◽  
Author(s):  
Mark G. Turner ◽  
John A. Reed ◽  
Robert Ryder ◽  
Joseph P. Veres
Keyword(s):  
Boundary Conditions ◽  
Fluid Dynamic ◽  
Thermodynamic Cycle ◽  
High Fidelity ◽  
Operating Characteristics ◽  
Cycle Model ◽  
Turbofan Engine ◽  
Engine Model ◽  
Cycle Simulation ◽  
Component Models

A Zero-D cycle simulation of the GE90-94B high bypass turbofan engine has been achieved utilizing mini-maps generated from a high-fidelity simulation. The simulation utilizes the Numerical Propulsion System Simulation (NPSS) thermodynamic cycle modeling system coupled to a high-fidelity full-engine model represented by a set of coupled 3D computational fluid dynamic (CFD) component models. Boundary conditions from the balanced, steady-state cycle model are used to define component boundary conditions in the full-engine model. Operating characteristics of the 3D component models are integrated into the cycle model via partial performance maps generated from the CFD flow solutions using one-dimensional meanline turbomachinery programs. This paper high-lights the generation of the highpressure compressor, booster, and fan partial performance maps, as well as turbine maps for the high pressure and low pressure turbine. These are actually “mini-maps” in the sense that they are developed only for a narrow operating range of the component. Results are compared between actual cycle data at a take-off condition and the comparable condition utilizing these mini-maps. The mini-maps are also presented with comparison to actual component data where possible.

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