# 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.

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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 ...
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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 ...
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### 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 ...
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### 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, \...
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### Locking phenomena for $P1 - P0$ elements

Consider the Stokes problem and the usual divergence operator $B:V \rightarrow Q'$, $\langle Bv, q\rangle = b(v,q)=(\operatorname{div} v,q)$ and its discrete versione $B_h : V_h \rightarrow Q_h'$. In ...
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### About the condition $\ker(B_h) \subset \ker(B)$ in mixed finite elements formulation

I'm studying mixed finite elements. The problem is a classical saddle-point one: we seek for $(u,p)$ in $V \times Q$: $$A u + B^t p = f$$ $$Bu = g$$ where $A: V \rightarrow V', B:V \rightarrow Q'$ ...
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### Understanding inf-sup conditions for classical saddle point problems

I'm studying the inf-sup conditions for saddle point problems. I'm referring to the usual one $$\begin{cases}Au + B^t p = f \\Bu=g \end{cases}$$ In the book I'm using (Ern - Guermond: Theory and ...
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### Confusion about preconditioner for incompressible Navier-Stokes equation with implicit-explicit method

Consider the time-dependent Navier-Stokes equation $$u_t + (u \cdot \nabla) u - \Delta u + \nabla p = f$$ $$\operatorname{div}(u)=0$$ Looking at deal.ii tutorials, I've notice that there are ...
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### What is the rationale of second-order finite volume discretization?

When it comes to a second-order accurate finite volume discretization of Navier-Stokes equations, which one of the two following rationales is adopted? 1- Second-order accuracy is a direct consequence ...
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### Why does including the pressure in this FVM for Stokes 2nd Problem lead to wrong solutions?

I'm trying to learn how to use finite volume methods and I want to solve a more general case of Stokes' second problem i.e. an infinite half-plane oscillating harmonically with no-slip boundary ...
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### Projection method FVM poisson part, adding source term

The idea of the method is to decompose the Navier-Stokes equation into the solenoidal and irrotational parts. $$\frac{\partial u}{\partial t}+u(\nabla \cdot u)=-\frac{1}{\rho}\nabla p+\nabla ^2 u$$ ...
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### Efficient schemes for solving the extended Saddle point problem

I am interested in knowing some efficient techniques for solving the following extended Saddle point problem. \begin{align} \begin{bmatrix} A & B^T & C^T \\ B & 0 & 0 \\ C & ...
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### Lumped mass matrices for higher-order finite elements for CFD

Given that some of the mass lumping techniques, for example, row-sum lumping does not produce practically viable lumped mass matrices for all the element shapes, what are the techniques used for mass ...
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### Stokes problem with imposed acceleration on boundaries (projection scheme)

I am trying to solve FSI problems with finite elements and using a projection scheme (I am taking as reference the review of Guermond: Guermond, J. L.; Minev, P.; Shen, Jie, An overview of ...
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### FDM on nonlinear PDEs

I'm working with a 2D Navier Stokes PDE in the unstabilized version - the equation is a linear equation of the type $\frac{∂u}{∂t} = F(u,t)$. In order to perform time discretization with FDM (finite ...
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### What kind of a researcher am I?

So far, I've worked a bit in modeling, simulations and simple lab experiments, and I've really enjoyed all three research methods to approach a single research question. I can write tricky (in terms ...
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### Numerical flow visualization in 2D for a moving boundary,

I have a rigid body that moves according to a set of governing ODEs, and I'd like to numerically visualize the vortices that are shed by this object. How could I proceed? I've been reading up on the ...
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### The relation between PDE order and discretization order

In Jasak's Ph.D. thesis (2000), a notion is given about discretization of a transport equation: For good accuracy, it is necessary for the order of the discretization to be equal to or higher than the ...
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### How to visualize the vorticity / flow for a rigid body moving through a fluid?

How can I write down two-dimensional Navier-Stokes equations for a simple rigid object immersed in a flow and freely falling due to gravity? I'm trying to view the vorticity that's induced by the ...
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### Pressure boundary conditions in Stokes Equation in 2D

I am solving the steady-state incompressible Stokes equations in 2D: $$\frac{\partial u_x}{\partial x} + \frac{\partial u_y}{\partial y} = 0,$$ \mu\left[\...