Implicit preconditioned high-order compact scheme for the simulation of the three-dimensional incompressible Navier-Stokes equations with pseudo-compressibility method

2011 ◽  
Vol 69 (7) ◽  
pp. 1165-1185 ◽  
Author(s):  
ZhanSen Qian ◽  
JingBai Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
High Order ◽  
Compact Scheme ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
High Order Compact Scheme

A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids

2017 ◽  
Vol 21 (5) ◽  
pp. 1231-1257 ◽  
Author(s):  
Jian Cheng ◽  
Xiaodong Liu ◽  
Tiegang Liu ◽  
Hong Luo
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
High Order ◽  
Navier Stokes ◽  
Attractive Alternative ◽  
Order Of Accuracy ◽  
Navier Stokes Equations ◽  
Hybrid Grids

AbstractA parallel, high-order direct Discontinuous Galerkin (DDG) method has been developed for solving the three dimensional compressible Navier-Stokes equations on 3D hybrid grids. The most distinguishing and attractive feature of DDG method lies in its simplicity in formulation and efficiency in computational cost. The formulation of the DDG discretization for 3D Navier-Stokes equations is detailed studied and the definition of characteristic length is also carefully examined and evaluated based on 3D hybrid grids. Accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. The capability in handling curved boundary geometry is also demonstrated. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results obtained indicate that the DDG method can achieve the designed order of accuracy and is able to deliver comparable results as the widely used BR2 scheme, clearly demonstrating that the DDG method provides an attractive alternative for solving the 3D compressible Navier-Stokes equations.

scholarly journals High-Order Finite-Element Framework for the Efficient Simulation of Multifluid Flows

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 203 ◽  
Author(s):  
Thibaut Metivet ◽  
Vincent Chabannes ◽  
Mourad Ismail ◽  
Christophe Prud’homme
Keyword(s):  
Finite Elements ◽  
Level Set ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Time Discretization ◽  
High Order ◽  
Navier Stokes ◽  
Mathematical Framework ◽  
Navier Stokes Equations ◽  
Coupling Approach

In this paper, we present a comprehensive framework for the simulation of Multifluid flows based on the implicit level-set representation of interfaces and on an efficient solving strategy of the Navier-Stokes equations. The mathematical framework relies on a modular coupling approach between the level-set advection and the fluid equations. The space discretization is performed with possibly high-order stable finite elements while the time discretization features implicit Backward Differentation Formulae of arbitrary order. This framework has been implemented within the Feel++ library, and features seamless distributed parallelism with fast assembly procedures for the algebraic systems and efficient preconditioning strategies for their resolution. We also present simulation results for a three-dimensional Multifluid benchmark, and highlight the importance of using high-order finite elements for the level-set discretization for problems involving the geometry of the interfaces, such as the curvature or its derivatives.

A High-Order Numerical Method to Study Three-Dimensional Hydrodynamics in a Natural River

2015 ◽  
Vol 7 (2) ◽  
pp. 180-195 ◽  
Author(s):  
Luyu Shen ◽  
Changgen Lu ◽  
Weiguo Wu ◽  
Shifeng Xue
Keyword(s):  
Numerical Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Simplec Algorithm ◽  
Dimensional Equation ◽  
Orthogonal Curvilinear Coordinate System

AbstractA high-order numerical method for three-dimensional hydrodynamics is presented. The present method applies high-order compact schemes in space and a Runge-Kutta scheme in time to solve the Reynolds-averaged Navier-Stokes equations with the k-ε turbulence model in an orthogonal curvilinear coordinate system. In addition, a two-dimensional equation is derived from the depth-averaged momentum equations to predict the water level. The proposed method is first validated by its application to simulate flow in a 180° curved laboratory flume. It is found that the simulated results agree with measurements and are better than those from SIMPLEC algorithm. Then the method is applied to study three-dimensional hydrodynamics in a natural river, and the simulated results are in accordance with measurements.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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