All Questions
Tagged with finite-difference fluid-dynamics
88
questions
1
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1
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62
views
How to calculate the force of solid applied by fluid? Using finite difference method, DNS, staggered grid, SIMPLE algorithm, immersive boundary
Problem
I am using finite difference method to solve classic problem of flow around cylinder, for validation of my group's immersive boundary method.
The common way to validate numerical method is ...
- 31
0
votes
1
answer
46
views
How to address the element face adjacent to boundaries when the finite difference method and marker-and-cell scheme are used to solve the Stokes flow?
The Stokes equations are
$$-\Delta \mathbf u + \nabla p = f \text{, in }\Omega,$$ and
$$ -\nabla \cdot \mathbf u = g, \text{ in } \Omega$$
where $\mathbf u = \left( u, v \right)$ is the flow ...
- 323
0
votes
0
answers
182
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discrete definition of curl $ \nabla \times \vec{A}$ on a 3D grid?
I have the data for 3D vector field $\vec{A}$ (with components $\vec{A_1}$, $\vec{A_2}$ and $\vec{A_3}$) sampled on a 3D grid with integer indices i, j and k.
Assuming that only the third component $\...
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5
votes
1
answer
245
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Solving simplified 1D plasma fluid equations with finite difference
The following two equations represent a simple model of a plasma where ions are immobile.
$$n\frac{\partial u}{\partial t}+nu\frac{\partial u}{\partial x}=n\frac{d\phi}{dx}-\theta\frac{\partial n}{\...
- 151
1
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0
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32
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How does Tannehill impose boundary conditions when coding the Parabolized Navier Stokes on an Implicit Finite Differences Scheme?
I'm trying to implement the scheme he describes on his book "Computational Fluid Mechanics and Heat Transfer" on Chap.9 and I'm having trouble imposing BC.
I don’t get how he imposes them. I ...
- 11
-1
votes
1
answer
154
views
The local and average Nusselt number in a square cavity
I am in the process of programming the local & average Nusselt number in a left vertical wall but my Matlab script gives me inappropriate values and it doesn't change with changing of Rayleigh ...
- 1
0
votes
1
answer
78
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How can I correctly determine velocity of a point inside a grid after using mixed finite element method to solve Poisson equation?
I am using the mixed finite element method (MFEM) to solve the Poisson equation:
$$\Delta h = 0,$$where $h$ denotes hydraulic pressure. The MFEM could determine the normal flux rate, $q_n$, through ...
- 323
2
votes
1
answer
211
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Shock Capturing Methods for Shallow Water Equations
I am looking for some help finding a numerical solution to the shallow water equations:
$\partial_tu+\partial_x(u^2/2+g\eta)=0$
$\partial_t \eta+\partial_x(u\eta)=0$.
where $u$ is the depth averaged ...
- 23
0
votes
1
answer
194
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Implementation of mixed hybrid finite element method
The mixed hybrid finite element method (MHFEM) is based on the mixed finite element method (MFEM). So, I'd recall the implementation of MFEM.
The mixed formulation of Poisson equation reads
$$\begin{...
- 323
2
votes
2
answers
100
views
Possible to use Iterative FD methods to solve a transformed non square domain [matlab]?
For the 2-D Poisson equation $$-(u_{xx}+u_{yy}) = f \ \ \text{where} f = 1$$
For boundary conditions
$$\frac{\partial u}{\partial n} = 0 \ \text{on AB and AD}$$
$$ u = 0 \ \ \ \text{on BC and CD no-...
- 23
3
votes
1
answer
142
views
Mineral dissolution and solute transport around a solid
I am trying to simulate solute transport of acid (HCl) and consequent mineral dissolution around a grain (calcite).
The governing equation for transport is the advection-diffusion equation, given as:
...
- 55
2
votes
0
answers
122
views
Solute transport around a solid obstacle
I am a newbie in CFD and single/multiphase flow and transport in general. As part of my quest to learn, I am trying to model solute transport around a solid object in the center of a 2D domain. The ...
- 55
3
votes
1
answer
89
views
Instability at the boundary of a finite difference simulation of a hyperbolic PDE
I want to simulate the hyperbolic partial differential equation
$$W_{tt} + V W_{tx} + k_E V W_x + k W_t = 0,$$
but I am having trouble finding a discrete analog of this equation which is numerically ...
- 131
1
vote
0
answers
62
views
Good non oscilliatory derivatives for an exsisting grid
I'm calculating the entropy production of a shockwave by utilizing the equations:
\begin{equation}
\sigma = J'_q\frac{\partial}{\partial x}\left(\frac{1}{T}\right) +\frac{1}{T}\frac{4\eta}{3}\left(\...
- 55
-3
votes
1
answer
156
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How to avoid negative concentration from numerical solution using FDM scheme?
$\frac{\partial C}{\partial t} + u \frac{\partial C}{\partial x} + w \frac{\partial C}{\partial x} = D \left(\frac{\partial^2C}{\partial x^2}+\frac{\partial^2C}{\partial y^2}\right)-C \cdot \left(\...
- 1