scholarly journals An Implicitly Balanced Hurricane Model with Physics-Based Preconditioning

2005 ◽  
Vol 133 (4) ◽  
pp. 1003-1022 ◽  
Author(s):  
J. M. Reisner ◽  
A. Mousseau ◽  
A. A. Wyszogrodzki ◽  
D. A. Knoll
Keyword(s):  
Linear System ◽  
Physical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Sound Waves ◽  
Time Step ◽  
Efficient Manner ◽  
First Order ◽  
Implicit Approach

A numerical framework for simulating hurricanes based upon solving a nonlinear equation set with an implicitly balanced solution procedure is described in this paper. The physical model is the Navier–Stokes equations plus a highly simplified and differentiable microphysics parameterization package. Because the method is fully implicit, the approach is able to employ time steps that result in Courant–Friedrichs–Lewy (CFL) numbers greater than one for advection, gravity, and sound waves; however, the dynamical time scale of the problem must still be respected for accuracy. The physical model is solved via the Jacobian-free Newton–Krylov (JFNK) method. The JFNK approach typically requires the approximate solution of a large linear system several times per time step. To increase the efficiency of the linear system solves, a physics-based preconditioner has been employed. To quantify the accuracy and efficiency of the new approach against traditional approaches, the implicitly balanced solver was first compared against semi-implicit approaches for the simulation of a precipitating moist bubble. The moist-bubble simulations demonstrated the ability of the implicitly balanced approach to achieve a given level of accuracy in a more efficient manner than either a first-order semi-implicit approach or a traditional leapfrog semi-implicit approach. This behavior is further illustrated in first-of-a-kind three-dimensional implicitly balanced hurricane simulations that reveal the first-order-in-time semi-implicit algorithm needs to take a time step at least 60 times smaller than the implicitly balanced algorithm to produce a comparable accuracy.

Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow

1969 ◽  
Vol 37 (4) ◽  
pp. 727-750 ◽  
Author(s):  
Gareth P. Williams
Keyword(s):  
Poisson Equation ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Wave Flow ◽  
Trigonometric Interpolation ◽  
Time Step ◽  
Navier Stokes Equations ◽  
The Poisson Equation

A method of numerically integrating the Navier-Stokes equations for certain three-dimensional incompressible flows is described. The technique is presented through application to the particular problem of describing thermal convection in a rotating annulus. The equations, in cylindrical polar co-ordinate form, are integrated with respect to time by a marching process, together with the solving of a Poisson equation for the pressure. A suitable form of the finite difference equations gives a computationally-stable long-term integration with reasonably faithful representation of the spatial and temporal characteristics of the flow.Trigonometric interpolation techniques provide accurate (discretely exact) solutions to the Poisson equation. By using an auxiliary algorithm for rapid evaluation of trigonometric transforms, the proportion of computation needed to solve the Poisson equation can be reduced to less than 25% of the total time needed to’ advance one time step. Computing on a UNIVAC 1108 machine, the flow can be advanced one time-step in 2 sec for a 14 × 14 × 14 grid upward to 96 sec for a 60 × 34 × 34 grid.As an example of the method, some features of a solution for steady wave flow in annulus convection are presented. The resemblance of this flow to the classical Eady wave is noted.

scholarly journals Three-Dimensional Simulation of Fluid–Structure Interaction Problems Using Monolithic Semi-Implicit Algorithm

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 94 ◽  
Author(s):  
Cornel Marius Murea
Keyword(s):  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Time Step ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Dimensional Simulation ◽  
Updated Lagrangian

A monolithic semi-implicit method is presented for three-dimensional simulation of fluid–structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier–Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. We use a global mesh for the fluid–structure domain where the fluid–structure interface is an interior boundary. The continuity of velocity at the interface is automatically satisfied by using globally continuous finite element for the velocity in the fluid–structure mesh. The method is fast because we solve only a linear system at each time step. Three-dimensional numerical tests are presented.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

Numerical Simulation of Asymmetric Exhaust Flows Using an Actuator Disc Blade Row Model

2002 ◽  
Author(s):  
Jianjun Liu
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Exhaust Hood ◽  
Navier Stokes Equations ◽  
Multigrid Algorithm ◽  
Blade Row ◽  
Actuator Disc

This paper describes the numerical simulation of the asymmetric exhaust flows by using a 3D viscous flow solver incorporating an actuator disc blade row model. The three dimensional Reynolds-Averaged Navier-Stokes equations are solved by using the TVD Lax-Wendroff scheme. The convergence to a steady state is speeded up by using the V-cycle multigrid algorithm. Turbulence eddy viscosity is estimated by the Baldwin-Lomax model. Multiblock method is applied to cope with the complicated physical domains. Actuator disc model is used to represent a turbine blade row and to achieve the required flow turning and entropy rise across the blade row. The solution procedure and the actuator disc boundary conditions are described. The stream traces in various sections of the exhaust hood are presented to demonstrate the complicity of the flow patterns existing in the exhaust hood.

Strongly Coupled Fluid-Structure Interactions via a New Navier-Stokes Method for Prediction of Vortex-Induced Vibrations

2005 ◽  
Author(s):  
Yannis Kallinderis ◽  
Hyung Taek Ahn
Keyword(s):  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Design Tool ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibrations ◽  
Offshore Industry

Numerical prediction of vortex-induced vibrations requires employment of the unsteady Navier-Stokes equations. Current Navier-Stokes solvers are quite expensive for three-dimensional flow-structure applications. Acceptance of Computational Fluid Dynamics as a design tool for the offshore industry requires improvements to current CFD methods in order to address the following important issues: (i) stability and computation cost of the numerical simulation process, (ii) restriction on the size of the allowable time-step due to the coupling of the flow and structure solution processes, (iii) excessive number of computational elements for 3-D applications, and (iv) accuracy and computational cost of turbulence models used for high Reynolds number flow. The above four problems are addressed via a new numerical method which employs strong coupling between the flow and the structure solutions. Special coupling is also employed between the Reynolds-averaged Navier-Stokes equations and the Spalart-Allmaras turbulence model. An element-type independent spatial discretization scheme is also presented which can handle general hybrid meshes consisting of hexahedra, prisms, pyramids, and tetrahedral.

Evaluation of numerical diffusion of the finite volume method when modelling surface waves

2019 ◽  
pp. 106-119
Author(s):  
Елена Сергеевна Тятюшкина ◽  
Андрей Сергеевич Козелков ◽  
Андрей Александрович Куркин ◽  
Вадим Викторович Курулин ◽  
Валентин Робертович Ефремов ◽  
...  
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Calculation Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Numerical Diffusion ◽  
Volume Method

Обсуждается применение метода конечных объемов при решении уравнений Навье-Стокса для моделирования поверхностных волн. Сформулирована задача о распространении поверхностных волн, которая используется для оценки численной диффузии в решении уравнений Навье-Стокса. Предлагается методика оценки численной диффузии, выражаемой коэффициентом уменьшения амплитуды волны при прохождении ею одной своей длины (коэффициентом затухания). Дана оценка размеров сетки и шага по времени, выраженных в безразмерных величинах относительно параметров волны, необходимых для обеспечения приемлемого значения коэффициента затухания. Показана степень влияния каждого из сеточных параметров на увеличение коэффициента затухания. The application of numerical simulation methods based on the solution of the full three-dimensional Navier-Stokes equations for modelling of wave propagation on the water surface requires the construction of a grid model containing countable nodes throughout the entire volume of water medium. Insufficient grid resolution leads to insufficient detailing of the fields of velocity and pressure, as well as volume fraction of the liquid, which increases the numerical diffusion of the method and, ultimately, leads to an underestimation of oscillation amplitudes of the medium. A large time step also results in a “blurring” of the solution and significantly reduces its stability, especially when using the schemes which compress the front of the media interface. This paper presents the results of an assessment of acceptable grid sizes and time steps expressed in dimensionless parameters with respect to the wave parameters necessary to ensure accuracy of the solution sufficient for geophysical applications. The estimate is given for the method of calculating three-dimensional multiphase flows with a free surface based on solving the Navier-Stokes equations in a one-velocity approximation based on a completely implicit connection between velocity and pressure using the finite volume method. The finite volume method for the numerical solution of the Navier-Stokes equations is implemented for use on arbitrary unstructured grids. The methodology for estimation of numerical diffusion of the calculation method is proposed. This estimation is expressed as a percentage of the wave amplitude decrease at the distance equal to the one wavelength. In turn the methodology is based on the parameters entered to estimate the acceptable grid sizes and time step for the calculation method. Based on the described methodology, the results of the estimation of the grid resolution in the horizontal and vertical directions, the estimation of the time step, and the evaluation of the influence of the discretization scheme of the convective term are presented.

Three-Dimensional Time-Marching Inviscid and Viscous Solutions for Unsteady Flows Around Vibrating Blades

1994 ◽  
Vol 116 (3) ◽  
pp. 469-476 ◽  
Author(s):  
L. He ◽  
J. D. Denton
Keyword(s):  
Thin Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Correction Method ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Blade Passage ◽  
Time Marching ◽  
Viscous Solutions

A three-dimensional nonlinear time-marching method of solving the thin-layer Navier–Stokes equations in a simplified form has been developed for blade flutter calculations. The discretization of the equations is made using the cell-vertex finite volume scheme in space and the four-stage Runge–Kutta scheme in time. Calculations are carried out in a single-blade-passage domain and the phase-shifted periodic condition is implemented by using the shape correction method. The three-dimensional unsteady Euler solution is obtained at conditions of zero viscosity, and is validated against a well-established three-dimensional semi-analytical method. For viscous solutions, the time-step limitation on the explicit temporal discretization scheme is effectively relaxed by using a time-consistent two-grid time-marching technique. A transonic rotor blade passage flow (with tip-leakage) is calculated using the present three-dimensional unsteady viscous solution method. Calculated steady flow results agree well with the corresponding experiment and with other calculations. Calculated unsteady loadings due to oscillations of the rotor blades reveal some notable three-dimensional viscous flow features. The feasibility of solving the simplified thin-layer Navier–Stokes solver for oscillating blade flows at practical conditions is demonstrated.

scholarly journals Four free surface algorithms for the 3D Navier–Stokes equations

2015 ◽  
Vol 17 (6) ◽  
pp. 845-856 ◽  
Author(s):  
Nils Reidar B. Olsen
Keyword(s):  
Wave Equation ◽  
Numerical Methods ◽  
Water Surface ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Free Water ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Free Water Surface

Four algorithms are described for computing a steady free water surface with the solution of the three-dimensional (3D) Navier–Stokes equations. The numerical methods are used in hydraulic engineering cases, typically spillways and river modelling. The algorithms were tested against a laboratory experiment of a v-shaped broad-crested weir. The complex geometry of the weir introduced three-dimensional effects, which the numerical methods handled with varying degrees of success. One of the methods tested was the classical volume of fluid (VOF) approach, implemented in the OpenFOAM software with a fixed grid. The other three algorithms used an adaptive grid that followed the free water surface. These methods were coded in the SSIIM 2 program and were based on water continuity, pressure differences and an implicit solution of the diffusive wave equation. The VOF method gave the best results compared with the experiments. However, this method requires a very short time step. Two of the investigated methods compute the water surface location implicitly and can therefore use a much longer time step. The method based on the diffusive wave equation has the disadvantage that the results depend on a calibrated friction factor. All four methods predicted the water depth over the weir with an average accuracy below 14%.

Analysis on Flutter Characteristics of Transonic Compressor Blade Row by a Fluid-Structure Coupled Method

2012 ◽  
Author(s):  
Mingming Zhang ◽  
Anping Hou ◽  
Sheng Zhou ◽  
Xiaodong Yang
Keyword(s):  
Phase Angle ◽  
Information Exchange ◽  
Stokes Equations ◽  
Aerodynamic Force ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Limit Cycle Oscillation ◽  
Time Step ◽  
Transonic Compressor ◽  
Blade Row

A time domain numerical approach is carried out to enhance the understanding of three dimensional blade row aeroelastic characteristics under the parallel computation. The vibration energy of unsteady aerodynamic force on the entire blade row is investigated using numerical solution of 3-D Navier-Stokes equations, coupled with structure finite element models for the blades to identify modal shapes and the structural deformations simultaneously. Interactions between fluid and structure are dealt with in a coupled manner, based on the interface information exchange until convergence in each time step. With this approach good agreement between the numerical results and the experimental data is observed. The flutter mechanism is analyzed according to deformation of the blades. The effect of inter-blade phase angle (IBPA) is included in the analysis by releasing the hypothesis of constant phase angle between adjacent blades in the traveling wave model. The results illustrate fully three dimensional unsteady nonlinear behaviors, such as limit-cycle oscillation. It is shown that all blades flutter at the same mode and frequency, but not at the same amplitude and IBPA. The analysis of the influence of different tip clearance gaps on the flutter characteristics of the blade row is also performed.

Modeling of Three-Dimensional Flow in Turning Channels

1984 ◽  
Vol 106 (3) ◽  
pp. 682-691 ◽  
Author(s):  
I. M. Khalil ◽  
H. G. Weber
Keyword(s):  
Stokes Equations ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Curved Channels

The structure of developing flows inside curved channels has been investigated numerically using the time-averaged Navier Stokes equations in three dimensions. The equations are solved in primitive variables using finite difference techniques. The solution procedure involves a combination of repeated space-marching integration of the governing equations and correction for elliptic effects between two marching sweeps. Type-dependent differencing is used to permit downstream marching even in the reverse-flow regions. The procedure is shown to allow efficient calculations of turbulent flow inside strongly curved channels as well as laminar flow inside a moderately curved passage. Results obtained in both cases indicate that the flow structure is strongly controlled by local imbalance between centrifugal forces and pressure gradients. Furthermore, distortion of primary flow due to migration of low momentum fluid caused by secondary flow is found to be largely dependent on the Reynolds number and Dean number. Comparison with experimental data is also included.

Sign in / Sign up

Export Citation Format

Share Document