Navier-Stokes Solution by New Compact Scheme for Incompressible Flows

In this paper we present effective preconditioning techniques for solving the nonsymmetric systems that arise from the discretization of the Navier–Stokes equations. These linear systems are solved using either Krylov subspace methods or the Richardson scheme. We demonstrate the effectiveness of our techniques in handling time-accurate as well as steady-state solutions. We also compare our solvers with those published previously.

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A Cartesian Explicit Solver for Complex Hydrodynamic Applications

Volume 2: CFD and VIV ◽

10.1115/omae2014-24680 ◽

2014 ◽

Author(s):

P. Bigay ◽

A. Bardin ◽

G. Oger ◽

D. Le Touzé

Keyword(s):

Level Set ◽

Incompressible Flows ◽

Stokes Equations ◽

Simulation Method ◽

Navier Stokes ◽

Viscous Effects ◽

Navier Stokes Equations ◽

Eddy Simulation ◽

Flow Past A Cylinder ◽

Explicit Solver

In order to efficiently address complex problems in hydrodynamics, the advances in the development of a new method are presented here. This method aims at finding a good compromise between computational efficiency, accuracy, and easy handling of complex geometries. The chosen method is an Explicit Cartesian Finite Volume method for Hydrodynamics (ECFVH) based on a compressible (hyperbolic) solver, with a ghost-cell method for geometry handling and a Level-set method for the treatment of biphase-flows. The explicit nature of the solver is obtained through a weakly-compressible approach chosen to simulate nearly-incompressible flows. The explicit cell-centered resolution allows for an efficient solving of very large simulations together with a straightforward handling of multi-physics. A characteristic flux method for solving the hyperbolic part of the Navier-Stokes equations is used. The treatment of arbitrary geometries is addressed in the hyperbolic and viscous framework. Viscous effects are computed via a finite difference computation of viscous fluxes and turbulent effects are addressed via a Large-Eddy Simulation method (LES). The Level-Set solver used to handle biphase flows is also presented. The solver is validated on 2-D test cases (flow past a cylinder, 2-D dam break) and future improvements are discussed.

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A Calculation Scheme for Three-Dimensional Viscous Incompressible Flows

Journal of Fluids Engineering ◽

10.1115/1.3242670 ◽

1987 ◽

Vol 109 (4) ◽

pp. 345-352 ◽

Cited By ~ 4

Author(s):

M. Reggio ◽

R. Camarero

Keyword(s):

Incompressible Flows ◽

Stokes Equations ◽

Three Dimensional ◽

Numerical Procedure ◽

Numerical Data ◽

Momentum Balance ◽

Navier Stokes ◽

Test Cases ◽

Pressure Gradients ◽

Navier Stokes Equations

A numerical procedure to solve three-dimensional incompressible flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of the time-dependent Navier-Stokes equations written for a general curvilinear coordiante system is adopted. The numerical scheme is based on an overlapping grid combined with opposed differencing for mass and pressure gradients. The pressure and the velocity components are stored at the same location: the center of the computational cell which is used for both mass and the momentum balance. The resulting scheme is stable and no oscillations in the velocity or pressure fields are detected. The method is applied to test cases of ducting and the results are compared with experimental and numerical data.

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A New Exponential Compact Scheme for the Two-Dimensional Unsteady Nonlinear Burgers’ and Navier-Stokes Equations in Polar Cylindrical Coordinates

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.oa-2020-0053 ◽

2021 ◽

Vol 14 (2) ◽

pp. 488-507

Author(s):

R.K. Mohanty

Keyword(s):

Stokes Equations ◽

Compact Scheme ◽

Navier Stokes ◽

Two Dimensional ◽

Cylindrical Coordinates ◽

Navier Stokes Equations

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Analytic reconstruction of a two-dimensional velocity field from an observed diffusive scalar

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.301 ◽

2019 ◽

Vol 871 ◽

pp. 755-774

Author(s):

Arjun Sharma ◽

Irina I. Rypina ◽

Ruth Musgrave ◽

George Haller

Keyword(s):

Velocity Field ◽

Ocean Circulation ◽

Incompressible Flows ◽

Circulation Model ◽

Scalar Fields ◽

Navier Stokes ◽

Two Dimensional ◽

Velocity Measurements ◽

Ocean Circulation Model ◽

Spatial Domains

Inverting an evolving diffusive scalar field to reconstruct the underlying velocity field is an underdetermined problem. Here we show, however, that for two-dimensional incompressible flows, this inverse problem can still be uniquely solved if high-resolution tracer measurements, as well as velocity measurements along a curve transverse to the instantaneous scalar contours, are available. Such measurements enable solving a system of partial differential equations for the velocity components by the method of characteristics. If the value of the scalar diffusivity is known, then knowledge of just one velocity component along a transverse initial curve is sufficient. These conclusions extend to the shallow-water equations and to flows with spatially dependent diffusivity. We illustrate our results on velocity reconstruction from tracer fields for planar Navier–Stokes flows and for a barotropic ocean circulation model. We also discuss the use of the proposed velocity reconstruction in oceanographic applications to extend localized velocity measurements to larger spatial domains with the help of remotely sensed scalar fields.

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The Investigation of a Sliding Mesh Model for Hydrodynamic Analysis of a SUBOFF Model in Turbulent Flow Fields

Journal of Marine Science and Engineering ◽

10.3390/jmse8100744 ◽

2020 ◽

Vol 8 (10) ◽

pp. 744

Author(s):

Yu-Hsien Lin ◽

Xian-Chen Li

Keyword(s):

Cfd Simulation ◽

Incompressible Flows ◽

Boussinesq Approximation ◽

Navier Stokes ◽

Hydrodynamic Characteristics ◽

Sliding Mesh ◽

Mesh Model ◽

Straight Line ◽

Frictional Coefficients ◽

Predictor Corrector

A computational fluid dynamics (CFD)-based simulation using a finite volume code for a full-appendage DARPA (Defense Advanced Research Projects Agency) SUBOFF model was investigated with a sliding mesh model in a multi-zone fluid domain. Unsteady Reynolds Averaged Navier–Stokes (URANS) equations were coupled with a Menter’s shear stress transport (SST) k-ω turbulence closure based on the Boussinesq approximation. In order to simulate unsteady motions and capture unsteady interactions, the sliding mesh model was employed to simulate flows in the fluid domain that contains multiple moving zones. The pressure-based solver, semi-implicit method for the pressure linked equations-consistent (SIMPLEC) algorithm was employed for incompressible flows based on the predictor-corrector approach in a segregated manner. After the grid independence test, the numerical simulation was validated by comparison with the published experimental data and other numerical results. In this study, the capability of the CFD simulation with the sliding mesh model was well demonstrated to conduct the straight-line towing tests by analyzing hydrodynamic characteristics, viz. resistance, vorticity, frictional coefficients, and pressure coefficients.

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Lr-LpStability of the Incompressible Flows with Nonzero Far-Field Velocity

Abstract and Applied Analysis ◽

10.1155/2011/856896 ◽

2011 ◽

Vol 2011 ◽

pp. 1-15 ◽

Cited By ~ 1

Author(s):

Jaiok Roh

Keyword(s):

Constant Velocity ◽

Incompressible Flows ◽

Temporal Stability ◽

Stationary Solutions ◽

Decay Rates ◽

Navier Stokes ◽

Far Field ◽

Spatial Direction ◽

Field Velocity ◽

The Stability

We consider the stability of stationary solutionswfor the exterior Navier-Stokes flows with a nonzero constant velocityu∞at infinity. Foru∞=0with nonzero stationary solutionw, Chen (1993), Kozono and Ogawa (1994), and Borchers and Miyakawa (1995) have studied the temporal stability inLpspaces for1<pand obtained good stability decay rates. For the spatial direction, we recently obtained some results. Foru∞≠0, Heywood (1970, 1972) and Masuda (1975) have studied the temporal stability inL2space. Shibata (1999) and Enomoto and Shibata (2005) have studied the temporal stability inLpspaces forp≥3. Then, Bae and Roh recently improved Enomoto and Shibata's results in some sense. In this paper, we improve Bae and Roh's result in the spacesLpforp>1and obtainLr-Lpstability as Kozono and Ogawa and Borchers and Miyakawa obtained foru∞=0.

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