# Questions tagged [fluid-dynamics]

The study of the properties of fluids and gases in motion

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55 views

### Choosing good modelling method for solving Boltzmann equation

I'm writing a solver for Boltzmann Equations (BE) including a force term in rarefied plasma, for my PhD. The aim is to see if an instability occurs inside an electric streamer (theoretically it should,...
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### Is the matrix exponential and the Jordan canonical form actually useful for solving differential equations?

All of my yearlong graduate-level Linear Algebra course notes from my professorāan algebraist/representation theoristāshows his love for the exponential map $e^A$ and the Jordan canonical formāand one ...
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### numerical instabilities in Fluid Dynamics, Finite Element Method

I'm looking for references to understand where the numerical instabilities come from in hydrodynamics in general, and notably when the PĆ©clet number: $Pe>1$. I'm using the finite element method. ...
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### Should I expect computational gains using a second-order splitting method here?

I am trying to solve a three-dimensional baroclinic transport problem. The hydrodynamic (three-dimensional shallow water) equations are: \begin{align} \nabla \cdot \vec{v} = 0, \tag{1} \\ \frac{\...
196 views

### Finite Element Stabilization for Drift-Diffusion/Advection-Diffusion Equations

I've tried my best to look through the relevant suggested similar questions when posting this, and hopefully this contains enough new material to not be considered a duplicate. I'm currently trying ...
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### Non-reflecting boundary conditions for compressible Navier-Stokes equations

I have some questions about the implementation of non-reflecting OUTFLOW boundary condition for Navier Stokes equations. Following Poinsot, Lele "Boundary Conditions for Direct Simulations of ...
275 views

### Simulation of surface tension-dominated interfaces

I want to simulate the shape of the free surface in a small fuel tank in microgravity, which is very slowly being emptied. The tank is not symmetric, the geometry is given by CAD (e.g. step file). ...
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### Transport Equation in a Tube: Source Term on Boundary

I'm modeling mass transport in a flow reactor. The flow reactor is a tube, which allows me to use cylindrical symmetry in solving the Convection-Diffusion-Reaction (CDR) Equation, which governs the ...
640 views

### Immersed boundary method

I'm trying to use immersed boundary method for the 3D flow problem (Navier-Stokes equations), but I'm maybe misunderstood something in this method. Main principles I took from this book. I use the ...
243 views

### N-body simulation for particles

I would like use N-body simulation for measure a torque on an object in a liquid (helium). It's a 2D study. On the site : http://www.browndeertechnology.com/docs/BDT_OpenCL_Tutorial_NBody-rev3.html I ...
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### How to estimate if a velocity field is statistically homogeneous?

For a 3D velocity field $\mathbf{u}$ obtained by direct numerical simulation. Assuming that the field is defined on a periodic domain $\mathcal{P}$ of periodicity $L_x$ in the $x$ direction, $L_y$ ...
410 views

### General case Kutta condition

I'm working on a 2D inviscid fluid simulation using a "panel method", with Potential being used to enforce the no-through boundary condition. I'm trying to incorporate the Kutta condition, which says ...
2k views

### Create 2D plot from two data sets in ParaView

I'm currently running a CFD simulation for an internal flow and need to compare my computed results to experimental data. The experimental data is saved as a comma separated file with columns for x,y,...
1k views

### 2D Stokes equation Code

Does anyone know where could I find a code (in Matlab or Mathematica, for example) for he Stokes equation in 2D? It has been solved numerically by so many people and referenced in so many paper that I ...
4k views

### What's the difference between grid-based and mesh-based methods for PDEs?

I am into computational fluid dynamics and so far I've found that the most common approaches to solve for the governing equations are Eulerian and Lagrangian. The former samples the domain at fixed ...
223 views

### What is eighth order central difference?

The origin of the question can be found here. I know the details about forward, backward and central differences. If $u$ is the variable, does eight order means it approximates the $u_{xx}$ using $u$...
375 views

### 2d Euler manufactured solutions

Where can I find manufactured solutions for the 2d Euler equations, with the complete analytical terms, including the Jacobian of the source term ?
173 views

### Why have specialised upwind schemes been developed to solve hyperbolic equations?

Are upwind schemes such as Godunov type methods superior to central differencing schemes? Do the reasons include superiority in modelling hyperbolic problems with Dirichlet BC's?
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### Automatic timestep adjustment in a CFD solver

I have developed my own 3D Finite Volume Navier-Stokes solver based on projection method for nonuniform grid. I am looking to incorporate automatic timestep adjustment at each time step based on ...
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### combination of field and particle methods for fluid dynamics

In numerical fluid dynamics there are field methods like finite-volume, finite-element, etc. and particle methods like Smoothed-Particle-Hydrodynamics ā SPH and others. Both approaches have advantages ...
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### Expected computational time for DNS computation of fluid flow

Using an established criterion involving capturing eddies down to the Kolmogorov length scale it can be reasoned that the order of grid points in the computational mesh needs to be $N^3 \ge Re^{9/4}$ ...
656 views

### Lattice Boltzmann methods vs Navier stokes/ other eulerian methods for *water* simulation

Note, there is already a question here, however the answers don't answer the original question, let alone specific considerations when dealing with nearly in-compressible fluids (water). Another ...
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### Can we simulate compressible flows by simple direct explicit calculation, without solving systems of linear equations (such as Poisson eq)?

Is this is plausible at all? It seems the most obvious/naive approach, so there's probably good reasons why it's not used - what are they? Viscosity is not important. Starting with inviscid Navier ...
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### What are acceptable boundary conditions for porous media flow?

I am attempting to simulate fluid flow through a porous foam. I would like to have no-slip boundary conditions on part of the boundary and free flow conditions on the inlet and outlet. Right now I am ...
2k views

### Patankar's algorithms for Numerical Heat Transfer and Fluid Flow

I am looking for the algorithm of Patankar (for example, SIMPLE, SIMPLER, SIMPLEC and PISO) written in Fortran for the simulation of heat transfer and fluid flow.
211 views

### Physical interpretation of divergence theorem

In a diverging pipe section like the following, the pipe of radius $r$ splits into two pipes of radius $r/2$. Consider a solute transported by convection from node 1. \frac{\partial C}{\partial t}...
914 views

### Simple methods for solving 2D steady incompressible flow?

I'm trying to make a CFD model where I can place a source and a sink anywhere in a grid and get the fluid flow rate across each cell boundary between those locations. I'm starting simple with a 3x3 ...
637 views

### Basic Finite Element Method (FEM) question: assembly and re-assembly

I'm reading up on the Finite Element Method (Zienkiewicz's Book), so I understand better what I'm doing in FEniCS and COMSOL. Currently, I'm wondering about this: Using FEM to solve fluid flow ...
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### Vortex Panel Method implementation

I'm trying to understand and implement panel methods for a two-dimensional airfoil. I haven't found yet a very detailed explanation on how to implement it, and there are some things I don't' still ...
185 views

### How is central difference scheme second-order accurate?

In an arbitrarily unstructured mesh, shown in the figure below, in the context of finite volume method, I want to obtain an approximation of $\phi_f$, where $N$ and $P$ are cell centers of adjacent ...