8/3/2019 Investigasi Numerik Pada Interaksi Struktur Keairan Menggunakan Metoda Berbasis Partikel Untuk Aplikasi Maritim_Marine Transport_Sun_Fanfan

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Numerical Investigations on Fluid-Structure InteractionsUsing Particle Based Methods for Marine Applications

Fanfan Sun ffs1g09@soton.ac.uk - School of Engineering SciencesSupervisors Dr. Mingyi Tan and Professor Jing Tang Xing

FSI Away Day 2010

Fluid Structure Interactions

Research Group

Objective

Theory

The formulation of SPH is often divided into two steps: integral representation

and then particle approximation.

Integral representation:

Particle approximation: and

here h is the smoothing length defining the influence area

Navier-Stokes equations:

(1)continuity equation ; (2)momentum equation; (3)energy equation

1). 2). 3).

Applying SPH method to equations 1 , 2 and 3

a). and b).

c).

considering unity property of kernel function showing below other forms of

SPH equation can be funded

Methodology

Investigation of Convergence of SPH

Conclusions

SPH is a pure meshfree, particle based method which is widely used for

fluid simulations especially rough sea motion simulations SPH approximations give accurate and reliable results

Fluid simulation will finally be coupled with structure simulation using,

for example, finite element method.

Introduction & Motivation

Many fluid-structure interaction problems often involve violent fluid

motions in marine engineering field, such as slamming and green water

when a ship travels in rough seas which can produce overall momentum

change and deformation of the hull. Hence, it is important to consider the

fluid-structure interactions, breaking waves and flow separations in order to

avoid damages caused by dynamic loads on the structures.

As it is difficult to obtain analytical solutions for such complicatedproblems, numerical methods and experiments are adopted ininvestigations. Traditional grid-based numerical methods like finite

element method have been developed but they are not efficient forlarge deformation problems. Particle based methods like SmoothedParticle Hydrodynamics (SPH) are an alternative to simulate fluidflows due to their Lagrangian and meshless properties.

To develop a numerical approach combing the smoothed particle

hydrodynamics method for fluid and other methods, FEM for example, for

structures to simulate violent fluid-structure interactions.

Figure 1: Rough sea slamming on offshore structure Figure 2: slamming on ship

(3.bp.blogspot.com/.../s200/freakwave.jpg)

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Hydrodynamics problems are generally expressed in the form of partial

differential equations which is normally impossible to obtain analytical

solutions for. Numerical solutions are necessary and SPH method is one of

the efficient method to solve this type of problems. The key ideas include:

Discreting the problem domain by a set of arbitrarily distributed particles.

No connectivity for these particles is needed (meshfree)

Approximating the field function by the integral representation method

(integral function representation)

Using particles to represent the kernel approximation by replacing the

integration term with the discrete particle volume (compact support)

Performing the particle approximation at every time step (adaptive)

Approximating every term related to field function in the PDEs to

produce a set of ODEs in discrete form with respect to time only

(Lagrangian)

Solving ODEs with explicit integration algorithm to obtain the time

history of all the field variables for all the particles

Convergence of the integral approximation and particle approximation

adopted in SPH is studied using a simple function f(x)=exp(-x) by

comparing the numerical results with analytical data

Figure 3. comparing analytical results and kernel approximation results.

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Figure 4. comparing analytical results and particle approximation results.

For integral

approximation,

Discretise the problem

domain into N points

with smoothing length

h. Results agrees with

analytical solution

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dxhxxWeexx

For particle

approximation,

Discretise the problem

domain into N particles

Results agrees with

analytical solution well

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