Questions tagged [fluid-dynamics]

The study of the properties of fluids and gases in motion

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0answers
81 views

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 professor—an algebraist/representation theorist—shows his love for the exponential map $e^A$ and the Jordan canonical form—and one ...
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25 views

Entropy of a spatially and temporally varying fluid system?

I'm trying to analyze the change in system thermodynamic entropy of an ideal gas system. For reference, I'm analyzing solution techniques for solving the 1D compressible Euler equations: $$ \partial_t ...
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66 views

Numerical scheme to calculate the normal mode of a set of hyperbolic PDEs?

I would like to solve the linearised, ideal, MHD equations, where the gas pressure is zero. $$\frac{\partial u_x}{\partial t}=v_A^2(x,z)\left[\nabla_{||}b_x - \frac{\partial b_{||}}{\partial x}\right],...
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1answer
134 views

Without positive definiteness, does an iterative solver work?

Question Does lacking positive definiteness of the matrix of coefficients in a system of equations, make using iterative solvers impractical? Description Using the finite volume method, I have ...
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1answer
78 views

Finite difference methods in cylindrical and spherical co-ordinate systems

I am quite familiar with finite difference schemes in cartesian coordinates. The key point here is that every point in the cartesian grid is treated equally as the spacing between consecutive points ...
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1answer
158 views

Can Julia be used to create a large-scale CFD software like OpenFOAM?

I have some experience with some programming languages like C/C++, Fortran, Python, etc but recently, I am getting interested in Julia. But, I am wondering if Julia could be used to create some large ...
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26 views

How to solve this mass transport diffusion equation?

My goal is to numerically solve the mass transport diffusion equation of the form: $$\ \nabla (D \nabla C) =0$$ $C$ is concentration and $D$ is the diffusivity constant. I was solving this for a ...
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1answer
94 views

Why is my Cahn-Hilliard simulation separating out so finely?

I am trying to simulate the Cahn-Hilliard equation using Python, but the 2 fluids aren't separating into big blobs, as desired, under any conditions. I'm setting up (what I think is) an orthogonal ...
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63 views

Open Boundary Conditions for Solving Navier Stokes in moving ALE domain

I'm trying to solve the problem of a body freely rising in a fluid due to gravity, the density of the body is just slightly less than that of the fluid. The body is rigid, so I have to solve a ...
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20 views

Convection equation expanded in Legendre polynomials

In some areas of physics, for example radiation transport in plasmas, it is beneficial to re-express the convection equation in terms of a Legendre polynomial expansion. This results in a set of ...
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26 views

Import stl file into Gmsh and create a 3d mesh for CFD

I am trying to develop a case study for teaching CFD. To this end, I am using OpenVSP, Gmsh and SU2. I have created a wing in OpenVSP, exported the CFD mesh as .stl file. Opened the .stl file in Gmsh ...
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What programming language should I choose and why?

I am a mechanical engineer, intermediated/advanced level in MATLAB and MATHEMATICA, and beginner in Python. I intend to get a PhD in aeroelasticity (FEM + CFD) and coding my own program. I intend to ...
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How does the “Stable Fluids” algorithm by Jos Stam relate to the SIMPLE and PISO algorithms?

The "Stable Fluids" paper (*) by Jos Stam starts by acknowledging that "Our method cannot be found in the computational fluids literature, since it is custom made for computer graphics applications. ...
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73 views

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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1answer
47 views

Numerical simulation of water layer over terrain

I'm looking for a grid-based numerical method that allows simulating water over a grid-based terrain, presumably something like shallow water equations. I have a square grid of terrain elevation ...
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3answers
148 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 ...
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32 views

First-principles benchmark of CFD solver

A decade ago I saw a ~20 coupled state + random number problem that was used as a benchmark for meteorological CFD tools. It had a fractal dimension (of the chaotic attractor) around 2.3, I think. I ...
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34 views

Decoupling of the fluid viscosity and incompressibility constraint in a partitioned scheme

I am new here and this is my very first question: I hope I respect all the criteria and rules. I am just getting started with partitioned approaches for solving FSI problems. I am interested in a ...
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55 views

Implementing Level Sets

I am trying to implement a basic level set program for fluid simulation in C++ and visualize it using SFML, so far I have the following simple program for propagating a circular curve: https://gist....
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1answer
189 views

Order of Accuracy Measurements on 1D Advection Methods

I am trying to learn about basics of computational fluid dynamics, at the moment on the simple example of linear advection in 1D. I am am currently testing the theoretical predictions of the order of ...
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32 views

Why it doesn't matter to use velocity gradient or shear rate tensor to calculate wall shear stress?

The wall shear stress is defined based on Matyka et. al. eq. A.4: $$\vec{\tau} = 2 \mu (\mathbf{S} \cdot \vec{n} - (\vec{n} \cdot \mathbf{S} \cdot \vec{n})\vec{n})$$ Where $\mathbf{S} = \frac{1}{2} (...
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1answer
134 views

Why lattice Boltzmann despite its huge number of mesh points still has worse accuracy in comparison to FEM for calculating wall shear stress?

I'm just doing a very simple experiment. I'm calculating wall shear stress based on Poiseuille flow for a pipe by using lattice Boltzmann method (LBM) and FEM to compare their values with the ...
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1answer
66 views

Filtering out outliers in a vector field [closed]

I have a vector field that represents a incompressible fluid flow (ie. divergence-free, ideally) that contains a certain percentage of vectors that are completely incorrect, due to the procedure used ...
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0answers
60 views

Defining appropriate test function spaces for the finite element solution of Euler's fluid equations

I have the following coupled equations for the conservation of mass and momentum of a compressible fluid : \begin{equation} \rho_t + (\rho u)_z = 0, \end{equation} $$ (\rho u)_t + (\rho u^2)_z + \...
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126 views

Velocity self-advection stability problem with QUICK upwind scheme

I'm trying to implement a finite-difference fluid solver (incompressible, inviscous) using the QUICK scheme for advection. Mostly I've been following the Norris thesis chapter 2 (https://ses.library....
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1answer
163 views

Application of Poiseuille equation

I'd like to know whether the Hagen-Poiseuille equation can be used to solve for the velocity of fluid when the Reynolds number (Re) is less than 1. From textbooks, I understand that the Hagen-...
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1answer
161 views

mesh dependence of numerical adjoint solution

I am solving the steady, two-dimensional adjoint Euler equations, $$A_x^T \partial_x \Psi + A_y^T \partial_y \Psi = 0$$, where $A_x = \partial F_x/\partial U$ and $A_y= \partial F_y/\partial U$ are ...
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149 views

Immersed boundary method in FEniCS?

I have looked at the FEniCS tutorials and documentation but I cannot find any mention to the possibility of implementing an immersed boundary method (IBM) for fluid dynamics. In particular, I want ...
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36 views

How to avoid density getting “deleted” in two way rigid body coupling with LBM CFD?

I've been reading this paper recently, which talks about using Lattice Boltzmann methods and two way coupling. Specifically, it outlines fluid solid coupling, and solid fluid coupling, and how simply ...
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1answer
94 views

Modelling flow through pipe networks

I'm trying to educate myself on modelling solute flows through pipe networks. This is a follow up of my previous post here $$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$ While ...
2
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1answer
98 views

Does mass balance hold in convective diffusion

I'm trying to understand how convection-diffusion equations are solved in pipe flow modules available in CFD solvers. $$ \frac{\partial C}{\partial t} + \nabla \cdot (\mathbf{v} C) = \nabla \cdot (D \...
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1answer
85 views

What is the correct way to calculate deviatoric stress tensor in lattice Boltzmann method?

Due to my previous question, where I asked about flux calculation in lattice Boltzmann (LB) method here, I have more or less same question for deviatoric stress tensor calculation due to pseudo-...
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48 views

Question regarding 1D implementation of the DG method

I'm pretty new to the DG method and have been writing a 1D code to help me understand the coding aspect. With respect a reference, I've been following these notes https://www3.nd.edu/~zxu2/...
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1answer
135 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 $u$...
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89 views

CFD and finite volume method: Dirichlet boundary conditions for the Euler equations

Please point me to an answer if one already exists, but after some searching, I still can't find the answer to what seems like a very simple question. There are plenty of references out there for ...
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1answer
48 views

Numerical integration of the dataset of a function

The energy equation for a spherically symmetric system is given by $$\mathscr{E}=\frac{v^2(r)}{2}+\frac{c_s^2(r)}{\gamma-1}+\phi(r)$$ where $\mathscr{E}$ is the total energy, $v$ is the velocity of ...
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1answer
158 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}...
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46 views

Simulating flow in a branched pipe

I am trying to simulate 1D advection and convection of a solute in the following blood vessel segment. I would like to know if this system can be simulated in COMSOL or MATLAB. I have used pdepe ...
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1answer
187 views

Implications of thermodynamic inconsistency in CFD calculations

During my PhD work, I had to use tabulated values of thermodynamic properties of gases in some Computational Fluid Dynamics (CFD in short) simulations. My tables are discretized in temperature and ...
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0answers
69 views

What is appropriate boundary condition for Poisson pressure equation?

I'm doing CFD simulations in unstructured grids. Well, it's a bit different from conventional unstructured grids that are used mainly in FEM or FVM as tetrahedral meshes. Mine is a voxelized mesh of ...
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58 views

What is Voronoi particle tracking?

I've been trying to track this down, but google is giving paywall papers that don't appear to be directly related to computational science, or simply don't explain the source algorithm. There's an ...
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1answer
105 views

Are there any commercial CFD codes that implement a Discontinuous Galerkin scheme?

I've been reading about the Discontinuous Galerkin discretization scheme and it's application to CFD for fluid flow. It seems to be a promising method for simulating turbulent flows, by using higher-...
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1answer
49 views

Smoothed Particle Hydrodynamics: Weird clustering of particles. Is that normal?

I implemented a rather simple SPH simulation using a cubic-spline-kernel and a simple non-iterative pressure solver as described in this PDF in equation 9. I followed algorithm 1 of that paper (...
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28 views

How to ensure values stay within range?

e.g. water in a height map Choosing a range with a margin of error for typical model behaviour seems practical. Could we instead (1). predict maximum values; or (2). have a natural maximum? 1. ...
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2answers
343 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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1answer
55 views

Should the derivative of an array be calculated array by array or element by element in CFD codes?

I am making my own finite difference computational magnetohydrodynamic code in Fortran 90. Looking at other codes they appear to calculate for example their $x$-derivatives, bb of their variables, e.g....
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23 views

Riemann solvers for metastable phases

Most Riemann solvers I've come across can solve the Riemann problem only under certain conditions such as convexity of the equation of state. But what happens if the fluid enters a metastable state or ...
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1answer
109 views

How to compute turbulent energy cascade

I need to compute the kinetic energy cascade using a finite volume solution in an equally spaced grid. I wonder if it is more correct to first compute the kinetic energy in the space (or time) domain, ...
2
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1answer
64 views

Confusion about Zabusky and Kruskal's stepper for the KdV equation

In Zabusky and Kruskal's paper about solitons, they derive the following update for the Korteweg de Vries equation (their footnote 6): \begin{align*} u_{i}^{j+1} = u_{i}^{j-1} - \frac{1}{3} \frac{k}{...
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0answers
95 views

Understanding MP-PIC implementation in OpenFOAM

The multiphase particle-in-cell (MP-PIC) method is characterized by mapping particle properties from the Lagrangian coordinates to the Eulerian grid. However, the implementation of this method in ...

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