2D Unstructured Mesh Finite Volume Method for Simulating Structural Dynamics

2013 ◽  
Vol 376 ◽  
pp. 345-348
Author(s):  
Miao Yu Hai ◽  
Xiao Hui Su ◽  
Yao Cao ◽  
Yong Zhao ◽  
Jian Tao Zhang
Keyword(s):  
Finite Volume ◽  
Unstructured Mesh ◽  
Solid Mechanics ◽  
Elastic Solid ◽  
Test Case ◽  
Time Step ◽  
Step Algorithm ◽  
Volume Method ◽  
Matrix Free ◽  
Fluidstructure Interaction

A novel procedure for calculating the dynamic response of elastic solid structures is presented. The ultimate aim of this study is to develop a consistent set of finite volume (FV) methods on unstructured meshes for the analysis of dynamic fluidstructure interaction (FSI). This paper describes a two-dimensional (2D) FV cell-vertex based method for dynamic solid mechanics. A novel matrix-free implicit scheme was developed using the Newmark method and dual time step algorithm and the model is validated with a 2D cantilever test case as well as a 2D plate one.

Application of Finite Volume Method for Solid Mechanics

2003 ◽  
Author(s):  
Bryce L. Fowler ◽  
Raymond K. Yee
Keyword(s):  
Finite Element ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Solid Mechanics ◽  
Preliminary Test ◽  
Test Case ◽  
Element Analysis ◽  
Vibration Isolators ◽  
Incompressible Materials ◽  
Volume Method

Polymers constitute a large class of nearly incompressible solid materials (i.e., Poisson’s Ratio near 0.5). These materials are often used as passive vibration isolators. Accurately modeling vibration isolators made of nearly incompressible materials has been extremely difficult with standard finite element analysis. This paper provides an alternative to the specialized finite element formulations currently used to model incompressible materials. The finite volume methodology of computational fluid dynamics is employed in this paper to solve the Hooke’s Law equations in solid mechanics. Test cases have been performed to evaluate the performance of finite volume method applied to solid mechanics problems. The formulation has been coded in Matlab for practical use. Based on the preliminary test case results, the finite volume formulation compares favorably to finite element method.

scholarly journals Inhibition of Ekortikus Island Expansion in Banyuasin Estuary, South Sumatra Modelling by Using Finite Volume Method with Unstructured Mesh

2015 ◽  
Vol 8 (3) ◽  
Author(s):  
Zulbahrum Caniago ◽  
Ibrahim. Eddy ◽  
Ridho. M R ◽  
Ngudiantoro Ngudiantoro ◽  
Bernas. Siti M
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Unstructured Mesh ◽  
Volume Method

scholarly journals Postprocessing of standard finite element velocity fields for accurate particle tracking applied to groundwater flow

2020 ◽  
Vol 24 (4) ◽  
pp. 1605-1624
Author(s):  
Philipp Selzer ◽  
Olaf A. Cirpka
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Particle Tracking ◽  
Mass Conservation ◽  
Velocity Fields ◽  
Test Case ◽  
Hydraulic Gradients ◽  
Volume Method

Abstract Particle tracking is a computationally advantageous and fast scheme to determine travel times and trajectories in subsurface hydrology. Accurate particle tracking requires element-wise mass-conservative, conforming velocity fields. This condition is not fulfilled by the standard linear Galerkin finite element method (FEM). We present a projection, which maps a non-conforming, element-wise given velocity field, computed on triangles and tetrahedra, onto a conforming velocity field in lowest-order Raviart-Thomas-Nédélec ($\mathcal {RTN}_{0}$ R T N 0 ) space, which meets the requirements of accurate particle tracking. The projection is based on minimizing the difference in the hydraulic gradients at the element centroids between the standard FEM solution and the hydraulic gradients consistent with the $\mathcal {RTN}_{0}$ R T N 0 velocity field imposing element-wise mass conservation. Using the conforming velocity field in $\mathcal {RTN}_{0}$ R T N 0 space on triangles and tetrahedra, we present semi-analytical particle tracking methods for divergent and non-divergent flow. We compare the results with those obtained by a cell-centered finite volume method defined for the same elements, and a test case considering hydraulic anisotropy to an analytical solution. The velocity fields and associated particle trajectories based on the projection of the standard FEM solution are comparable to those resulting from the finite volume method, but the projected fields are smoother within zones of piecewise uniform hydraulic conductivity. While the $\mathcal {RTN}_{0}$ R T N 0 -projected standard FEM solution is thus more accurate, the computational costs of the cell-centered finite volume approach are considerably smaller.

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.

An integrated algorithm for hypersonic fluid–thermal–structural analysis of aerodynamically heated cylindrical leading edge

2019 ◽  
Vol 233 (14) ◽  
pp. 5177-5191 ◽  
Author(s):  
Jiawei Li ◽  
Jiangfeng Wang
Keyword(s):  
Structural Analysis ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Maximum Temperature ◽  
Aerodynamic Heating ◽  
Hypersonic Vehicles ◽  
Time Step ◽  
Heated Cylinder ◽  
Leading Edges ◽  
Volume Method

The accurate and efficient prediction of the fluid–thermal–structural performance of thermal protection systems on hypersonic vehicles to protect against severe aerodynamic heating is attracting increasing worldwide attention. In this paper, a new integrated fluid-structural-thermal investigation based on the finite volume method is proposed to study the thermal behavior of aerodynamically heated cylinder leading edges in hypersonic flows. A unified integral equation system is developed based on the governing equations for the physical processes of aerodynamic heating and structural heat transfer, which is resolved by using an up-wind finite volume method and a new two-thermal-resistance model in one integrated, vectorized computer program. To demonstrate its capability and reliability, applications for steady/unsteady fluid–thermal–structural analysis are demonstrated on aerodynamically heated cylinder leading edges at Ma 6.47. The results show that the steady maximum temperature of the cylinder can reach approximately 648 K at the stagnation point, and the unsteady results are in good agreement with the experimental data and related references. Compared with the partitioned approach, the integrated method shows better computational stability with relatively small sensitivity to mesh scale and time step, reducing the computation time for the same unsteady case by approximately 50%. The present study indicates that the integrated approach has potential for significant improvements and efficiency in predicting long-endurance fluid-structural-thermal problems of hypersonic vehicles.

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