Questions tagged [navier-stokes]
Questions about solution methods of the Navier-Stokes equations, related physical constants and non-dimensional number. Also special methods to solve the equations including the assumptions and their implementation in order to simplify them. Also, questions regarding modelling of the non-linear term, coefficients of these model can be subjective of this title.
152
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Good references for the P3/P1dc element
I am struggling to find some good references for the P3/P1dc element (cubic element for velocity and linear piecewise discontinuous for pressure) for the Stokes/Navier-Stokes equations.
Is there a ...
- 964
1
vote
1
answer
62
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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
2
votes
1
answer
105
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Why can the weak forms of the Stokes and continuity equations be combined into a single equation?
Consider this Stokes equations,
$$
\left\{
\begin{array}{r}
- \mu \Delta \vec{u} + \nabla P = \vec{f} \\
\nabla \cdot \vec{u} = 0
\end{array}
\right.
$$
Weak form I is:
$$
\...
- 21
1
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1
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How to approximate the flux when using finite volumes?
How to approximate flux $F(u)\cdot n$ where $n$ denotes the unit normal outward when using finite volumes?
$$\int_{\sigma} F(u) \cdot \boldsymbol{n}_{K, \sigma} \mathrm{d} \gamma(x)$$
- 21
3
votes
1
answer
160
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Non-standard boundary condition for incompressible Navier Stokes
I am having difficulties applying the boundary condition
$$\frac{\partial \vec{V}}{\partial t} + u\frac{\partial \vec{V}}{\partial x} = \frac{1}{\operatorname{Re}}\frac{\partial ^2 \vec{V}}{\partial y^...
- 362
2
votes
0
answers
109
views
Using FEM for Navier-Stokes equation
I'm typically using FEM for solid mechanics problems and when I look into performing fluid-structure interaction, I saw they use FV or SPH method for the fluid domain. I'm not an expert in fluid ...
- 289
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
3
votes
1
answer
209
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Projection (or fractional-step) methods Vs coupled method for incompressible Navier-Stokes
My question is in the context of the finite element method.
Incompressible Navier-Stokes equations can be solved using the coupled method or projection/fractional step methods. Each method has its ...
- 964
2
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1
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How do the navier stoke equations model materials who "forget" their original form?
Sorry for the screenshot but I don't want to try to format this on latex:
We have this annotation of the Navier-Stokes equations:
I am particularly puzzled by the viscosity/stress term. For an ...
- 273
1
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0
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How to calculate the reynolds number for airborne wind energy system?
I am asking for some help on how to calculate the reynolds number for an AWES. I know the formula of Re=rhovl/viscosity. I have selected the air foil as Clark y with chord length 3.72m (which will be ...
- 11
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0
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93
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navier-stokes equations in semi-discrete form
Can someone point me to where the Navier-Stokes equations in 2D, both compressible and incompressible are written in semi-discrete form? I'm doing reduced order modelling and I need to write them down ...
- 760
1
vote
0
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167
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Partition of unity in FEM with bubble functions
In FEM with bubble functions, the field ($\boldsymbol{u}$) is approximated as a linear combination of the standard one ($\tilde{\boldsymbol{u}}$) plus the bubble field ($\boldsymbol{u}^b$). That is,
\...
- 964
1
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1
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How to implement pressure stabilization in matlab while solving steady stokes equation
the equation is $$
\left\{\begin{array}{l}
-\nabla \cdot \mathbb{T}(\mathbf{u}, p)=\mathbf{f} \text { in } \Omega, \\
\nabla \cdot \mathbf{u}=0 \text { in } \Omega, \\
\mathbf{u}=\mathbf{g} \text { on ...
- 193
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votes
0
answers
50
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How to specify the value of pressure in a point in solving steady stokes equation numerically?
I try to solve the steady-Stokes equation numerically on , that is
\begin{aligned}
-\nabla \cdot \mathbb{T}(\mathbf{u}, p) & =\mathbf{f} \quad \text { on } \Omega=[0,1]*[-0.25,0], \\
\nabla \cdot \...
- 193
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1
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Decoupling Stokes problem into two problems: velocity and pressure, using FEM
I have seen finite difference methods for fluid equations (Stokes and Navier--Stokes) that solve a pressure problem first and then a fluid problem. That is, although they solve two different problems, ...
- 515