Questions tagged [fluid-dynamics]
The study of the properties of fluids and gases in motion
476
questions
-1
votes
1answer
139 views
Finite Element - Flux Calculation
I am solving an advection-diffusion equation using the FEM and am having trouble calculating my fluxes.
I start with the equation,
$$\frac{\partial n}{\partial t} = \frac{\partial j_{n}}{\partial x}\...
7
votes
1answer
535 views
Time discretization of the variational formulation of the Navier-Stokes equation
I've asked this question on mathoverflow too.
Let
$T>0$
$I:=(0,T]$
$d\in\mathbb N$
$\Lambda\subseteq\mathbb R^d$ be nonempty and open, $$\mathcal V:=\left\{\phi\in C_c^\infty(\Lambda,\mathbb R^d):...
2
votes
3answers
531 views
Finite volume piecewise linear 2D advection develops instability
I'm developing a finite volume solver for the simple twodimensional advection equation with constant velocities $u, v$ and constant mesh spaces $\Delta x$:
$$ \frac{\partial \rho}{\partial t} + u \...
1
vote
0answers
31 views
Immersed boundary method in FEniCS?
I have looked at the FEniCS tutorials and documentation but I cannot find any mention to the possibility of implementing an immersed boundary method (IBM) for fluid dynamics.
In particular, I want ...
3
votes
1answer
61 views
Modelling flow through pipe networks
I'm trying to educate myself on modelling solute flows through pipe networks.
This is a follow up of my previous post here
$$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$
While ...
1
vote
0answers
32 views
How to avoid density getting “deleted” in two way rigid body coupling with LBM CFD?
I've been reading this paper recently, which talks about using Lattice Boltzmann methods and two way coupling. Specifically, it outlines fluid solid coupling, and solid fluid coupling, and how simply ...
2
votes
1answer
71 views
Does mass balance hold in convective diffusion
I'm trying to understand how convection-diffusion equations are solved in pipe flow modules available in CFD solvers.
$$
\frac{\partial C}{\partial t} + \nabla \cdot (\mathbf{v} C) = \nabla \cdot (D \...
2
votes
0answers
15 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-...
1
vote
0answers
36 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/...
2
votes
1answer
84 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 $u$...
2
votes
1answer
42 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 ...
2
votes
0answers
43 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 ...
2
votes
1answer
118 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}...
11
votes
1answer
179 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 ...
0
votes
0answers
39 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 ...
3
votes
1answer
332 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 ...
1
vote
2answers
161 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 ...
2
votes
0answers
56 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 ...
1
vote
1answer
84 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-...
1
vote
1answer
294 views
1-D turbulent energy spectra in homogeneous direction (non-isotropic)
I am trying to compute the one-dimensional energy spectra for my channel-flow simulation. I have already written a post-processing script to achieve this; however, I need to validate my code before ...
0
votes
0answers
26 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 ...
-1
votes
1answer
42 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 (...
0
votes
0answers
24 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. ...
3
votes
5answers
2k views
What is the difference between MATLAB and FORTRAN?
In our university some Ph.D students for computational methods prefer FORTRAN over MATLAB. I can't understand why? What is the difference between them when are used in computational methods like ...
1
vote
1answer
52 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....
2
votes
0answers
22 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 ...
1
vote
1answer
93 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, ...
6
votes
3answers
10k views
The real myth of GPU (specifically CUDA) really speed up FEM/CFD
Now I have been believing that FEM/CFD is supposed to be faster on a GPU unit - here I am using CUDA as solid example. However, I have not been able to find a convincing paper where the benchmark ...
2
votes
1answer
48 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}{...
2
votes
0answers
47 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 ...
1
vote
0answers
25 views
Finite difference/element method : time step and spatial resolution close to a finite singularity
I'm using the finite element method (FEM), but my question is quite a global question. It's related to this question but it is not the same.
Let's assume we have this equation : $$\partial_t c - u\...
3
votes
0answers
82 views
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 Péclet number: $Pe>1$. I'm using the finite element method.
...
1
vote
0answers
23 views
Solution errors when refining a static grid: Continuous vs. step-wise refinement
Let's assume I am working on a 2-D domain on $R^2$, with my coordinates $x \in[-1,1]$, $y \in[-1,1]$ and I want to solve a popular CFD problem, like the shallow water system or the Euler system.
At $x=...
0
votes
1answer
78 views
What's a time centered Riemann problem?
I am trying to understand the meshless methods as described in https://arxiv.org/pdf/1409.7395.pdf. I'm having trouble understanding the following step: (Page 7, just after equation 17)
Now, rather ...
7
votes
1answer
211 views
Do computational scientists typically also become domain experts?
Let's say I'm interested in fluid dynamics, specifically in fluid-structure interactions -- and I want to get into modeling, simulations and experiments. I am a mathematics student by training, ...
1
vote
1answer
59 views
What is the exponential trick to include laplacian term in Rayleigh-Bernard simulation
I have come across a Rayleigh-Bernard simulation code which doesn't have the laplacian term but an integrating factor (in the exponential form) containing viscosity and diffusivity. I found out that ...
0
votes
1answer
85 views
Well-posedness of Navier-Stokes equation
Before running a simulation for turbulence (e.g Rayleigh-Benard Convection), how do we check for well-posedness of Navier-Stokes with other equations for a given boundary condition??
Can someone ...
5
votes
1answer
471 views
Finite volume a posteriori error estimation
I'm wondering what alternatives there are to a grid convergence study to judge solution accuracy for a given grid resolution when doing steady-state RANS simulations on an automatically generated ...
1
vote
1answer
348 views
Difficult bug in my 2D Compressible Euler solver
For the past few days, I have been writing a numerical solver for the 2D compressible Euler equations for an ideal gas. My numerical method has been the Local Lax Friedrichs or "Rusanov's method." ...
3
votes
1answer
339 views
Limitations with dynamical systems vs. PDEs?
As a computational scientist, are there limitations to studying dynamical systems — systems of odes in which each state variable evolves with time — compared to studying PDEs?
For instance, it seems ...
2
votes
1answer
124 views
Why don't we call the simulation “a model for …”?
When a set of model equations, e.g. some coupled differential equations, has solutions that behave in ways similar to real-life phenomena such as blood flow in the heart, a wave movement, or a plate ...
0
votes
2answers
264 views
Boundary conditions for streamlines in enclosed flow
I am trying to solve Lid driven square cavity flow problem of Stokes equation using finite element method. I have boundary conditions for velocity as zeros on every boundary but u=1 on top boundary. ...
1
vote
0answers
34 views
Pseudospectral method for Rayleigh-Benard with constant temperature gradient
$$
\nabla\cdot \mathbf{u} = 0 \\
\frac{\partial \mathbf{u}}{\partial t}+\left(\mathbf{u}\cdot \nabla\right)\mathbf{u} = -\nabla p+\nu\nabla^2\mathbf{u}+\alpha g\theta\mathbf{e}_z\\
\frac{\partial\...
2
votes
0answers
42 views
Verification on pressure predictor method for CFD code
I have developed a python code for a lid-drive cavity model. However, my results are not converging. The algorithm of my code looks like this:
Euler Momentum Equation looks like this:
$$\frac{u^{n+1}...
0
votes
0answers
36 views
Is semi-Lagrangian 1D advection identical to upwind Euler, when $|u|<\Delta x/\Delta t$?
This looked true to me, I worked through the algebra for 1D and confirmed it. But no one seems to mention it, so maybe I'm missing something...
I'm using Bridson's SIGGRAPH 2007 course notes. [5MB ...
2
votes
0answers
56 views
Solving a simple Shallow Water model
Hi. I have a question at Mathematics and they suggested post here, once it's not common. I transcript as following. Many thanks
I need to solve with basic methods this simple Shallow Water Model:
$...
6
votes
0answers
120 views
What are some good debugging habits for numerical simulation?
I'm currently writing a lid drive cavity CFD code on python. Currently, my code has some issues (values jumping bear b.c). I was wondering what are some good habits in debugging numerical codes. ...
0
votes
0answers
8 views
Universal formulation of adiabatic equations of state in compresible finite-volume simultions
I code some finite element solver which should work for broad variety of materials (i.e. gas, liquid, solid, plasma) and large span of compressions resp. densities. I want to simulate things like ...
1
vote
1answer
152 views
What will be the impact of quantum computing on existing numerical techniques (e.g. CFD)?
Quantum computing seems to be a very active and promising development area in computer science. However, I am curious as to what impact (if any) quantum computing will have on existing classical ...
1
vote
0answers
47 views
WENO scheme on curvilinear coordinates
I've been developing a curvilinear FVM code. So far I've implemented the PPM scheme and am looking into adding WENO schemes. So far I've been discretizing the grid metrics using a second-order central....
