Questions tagged [fluid-dynamics]
The study of the properties of fluids and gases in motion
0
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0answers
24 views
MHD - How to impose a solid, perfect insulator as a boundary condition?
Consider the following MHD equations:
$$\frac{\partial \rho}{\partial t}+\nabla\cdot(\rho\vec{u})=0,$$
$$\rho\frac{D \vec{u}}{Dt}=\vec{j}\times\vec{B}-\nabla p,$$
$$\frac{\partial\vec{B}}{\partial t}=\...
1
vote
0answers
43 views
How to simulate water, falling under gravity, and impinging on a curved surface, which is kept/present in a domain, containing air?
TL;DR: How do I simulate a hole, at the bottom of a (full) water tank?
I am attempting to simulate water, flowing out of a hole/slit, at the bottom of a tank (Water Domain) (under the influence of ...
0
votes
1answer
44 views
Python Finite Difference Schemes for 1D Heat Equation: How to express for loop using numpy expression
Hello all,
I've recently been introduced to Python and Numpy, and am still a beginner in applying it for numerical methods. I've been performing simple 1D diffusion computations. I suppose my ...
-1
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0answers
42 views
How to discretize continuity equation with velocity calculated using Darcy's law?
$$
\partial_t(\epsilon_g\rho_g)+\partial_x\cdot(\epsilon_g\rho_g\mathbf{v}_g)=\Pi
$$
I want to program normal continuity equation and Darcy's law to calculate velocity.
$$
\mathbf{v}_g=-\frac{1}{\...
0
votes
2answers
56 views
TVD for temporal dicretisation
I have come across schemes where TVD (with flux limiters) is used for spatial discretisation along with Runge-kutta for Temporal discretisation.
Can TVD be used for Temporal discretisation? If so ...
-1
votes
0answers
40 views
Choice of initial condition
I am trying to simulate the following system.
$$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2}-v\frac{\partial C}{\partial x}$$
with initial condition
$$c(x,0) = C_o$$
and ...
-1
votes
0answers
16 views
Modelling hinge joint for Six DOF solver in OpenFOAM
I need to perform computation using Six DOF solver in 'OpenFOAM’. There are two 2D rigid solid bodies in quiescent water domain, having hinge joint in between them. Bodies are free to move in the ...
0
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1answer
46 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 ...
2
votes
0answers
47 views
Why do stabilized formulations for the Navier-Stokes equation maintain the convergence rate for high order polynomial interpolation?
I have a quick questions which has been troubling me lately.
When reading the FENICS Finite Element Book they assess various approaches to solver the Stokes equation. Obviously, they discuss the ...
3
votes
2answers
134 views
Asymptotic error of forward Euler
I'm trying to understand the asymptotic error behaviour of forward Euler (finite difference method), as timesteps are decreased (refined), so I feel trust in the method of manufactured solutions (MMS)....
-1
votes
1answer
35 views
Modeling Diodes in Autodesk CFD
I'm extremely new to Autodesk CFD, and I'm working on a project that deals with diodes heating up and cooling down based on a fixed temperature regulated by a temperature switch. Basically, I have a ...
2
votes
1answer
85 views
Numerically solving a partial differential equation
I am trying to numerically solve the following PDE,
$$\frac{\partial u^A}{\partial t} = c_1\frac{\partial^2 u^A}{\partial^2x} \,,$$
where $c_1$ is a constant. The above can be discretized using the ...
1
vote
2answers
65 views
Guaranteed equality between binary results with increasing MPI processes
Testing on an MPI scientific code for compressible flow dynamics I noticed that the results may depend on the number of processors used for the calculation. In fact, comparing the binary files they ...
1
vote
0answers
35 views
Has there been a comparison bewteen SIMPLE/SIMPLER and JFNK for steady CFD?
I'm looking for a comparison between the Jacobian-Free Newton-Krylov (JFNK) method performance compared to the conventional CFD nonlinear solution methodologies like SIMPLE.
Does anyone know if such ...
2
votes
0answers
38 views
WENO methods: why the characteristic wise method resulting big errors?
I was doing my research/project using WENO as the limiter in finite volume methods to solve hyperbolic conservation law. I have no idea why the result in the characteristic wise method has a big error ...
3
votes
1answer
52 views
Plotting or Visualizing a Higher dimensional vector field
I am trying to visualize a higher dimensional vector field. Is there a way to do this. I asked this question here, I was told to post it here.
As an example, one can use
$$\begin{eqnarray}
\dot{x}...
4
votes
1answer
65 views
How to go from turbulent RANS to laminar Navier-Stokes and Euler
SU2 is an open-source CFD suite that is built around a RANS-solver. The main PDE that is solved, is the following:
$$
\frac{\partial}{\partial t} \mathbf{U} + \nabla \cdot \mathbf{F^c} - \nabla \cdot ...
1
vote
0answers
29 views
How to remove sigularities from 3D Vortex Lattice Method
I'm trying to solve aerodynamics of whole aircraft by vortex lattice method (or deeper here). The problem is that sometimes trailing vortex filaments from Horse Shoe Vortexes of main wing hits panels ...
0
votes
0answers
62 views
Oscillations in force coefficients from CFD simulations
I have carried out a CFD simulation (with finite volume method) to investigate the unsteady force enforced to the vehicle body. The horizontal tail keeps flapping in sinusoidal function. As a result, ...
3
votes
0answers
43 views
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{\...
2
votes
1answer
81 views
When writing a research article, how to deal with deviations from theoretical expectations due to numerical errors?
We research the aerodynamics of the vehicle. Usually, there exists turbulence, which will cause the time-varying measurement of the force. The unsteady flow field determines we could not get a ...
1
vote
2answers
101 views
Demo example for OpenFOAM with CUDA
I am looking for a simple usage example/demo of OpenFOAM + CUDA and would like to understand how exactly OpenFOAM benefits from CUDA. The thing is I do not have any background in fluid dynamics and so ...
1
vote
1answer
31 views
Loss of energy when using Roe Solver for solving onedimensional Shallow Water Equations
I have written a Roe solver with Harten entropy fix code in Matlab to numerically solve the one-dimensional Shallow Water Equations. :
\begin{eqnarray}
\dfrac{\partial h(x,t)}{\partial t} + \dfrac{\...
0
votes
1answer
65 views
Poincare map for Arnold-Beltrami-Childress Magnetic Field in Python
I want to plot the Poincare map for Arnold-Beltrami-Childress magnetic field for parameters $A=1, B=0.816, C=0.5773$ in Python for the Poincare section $z=0$.
Also, I am not able to understand what ...
1
vote
0answers
73 views
Comparison between FEM and FDM methods for flow simulations
What are the main differences between finite element and finite difference approach for incompressible flow simulations? I have a vague idea about how FE methods rely on minimizing the residual over ...
4
votes
0answers
134 views
A good 2D finite difference for the continuity equation
How could I go about solving the continuity equation below in 2D?
$$\frac{\partial \rho}{\partial t} + \nabla \cdot \left(\rho u\right)=0$$
I saw that a similar question was posted here: A good ...
2
votes
1answer
75 views
build a simple incompressible solver with spectral method
I am trying to build a simple solver for the incompressible fluid in a periodic box to learn the spectral method. I am following the textbook (Peyret R. Spectral methods for incompressible viscous ...
2
votes
2answers
105 views
Algorithm to generate water flow map, given a terrain
I've posted the same question at GameDev Stack Exchange, but unfortunately I am not getting any response. So I am going to post ( and reword) it here. Hopefully I can get an answer!
I have a terrain (...
0
votes
2answers
99 views
Conservative formulation for compact finite difference schemes
At the Section 4.2 of this paper (which is very well known in the computational fluid dynamic community), the author claims that it is enough, for the compact finite difference formulation in eq. 4.2....
1
vote
0answers
48 views
fourth order Poisson iterative solver --in Matlab
I want to calculate the stream function $\psi$ starting from a velocity field $(u,v)$ (such that $u=-\frac{\partial\psi}{\partial y}$ and $v=\frac{\partial\psi}{\partial x}$). I thus calculate the ...
3
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0answers
122 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 ...
1
vote
0answers
49 views
Stokes flow around rigid body
I'm trying to simulate Stokes flow in 2D around an arbitrary polygon (representing a rigid body). I'd like to get both the effect of the body on the flow velocity and the forces on the body by the ...
0
votes
1answer
119 views
Unphysical Behaviour Characteristic-Wise WENO5-Z
I am currently working on a scheme that uses finite differences WENO5-Z with 3rd Order Runge-Kutta time integration for solving the Euler equations. The code projects the conserved variables and ...
1
vote
2answers
301 views
Which python library for GPU sparse linear system solver library
I have a fluid dynamic solver written in python which I want to accelerate by moving the most expensive computations to the GPU. Ideally all arrays and sparse matrices used in my code should remain on ...
1
vote
1answer
62 views
Defining dimensionless tempearture for Periodic flow systems
Given a flow inside a square duct with constant temperature at the walls $(T_{w1} = T_{w2} = T_w)$ the physical property in terms of temperature that repeats itself in a periodic fashion is the $\...
3
votes
0answers
80 views
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 ...
2
votes
0answers
84 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).
...
0
votes
2answers
100 views
Second derivative in coordinate invariant form
To solve stationary, incompressible, inviscid and irrotational flow around a circular cylinder, I am using general coordinates. Since the flow is symmetrical, we only consider the upper half of the ...
1
vote
2answers
126 views
Find classical solution of transport equation with FDM
We know the classical solution of transport equation is determined by one initial (boundary?) condition, for example, the solution of
$$\frac{\partial u(t,x)}{\partial t}+\frac{\partial u(t,x)}{\...
0
votes
1answer
255 views
Finite volume software packages
There are many software packages for the finite element method, of which the most popular are listed e.g. on Wikipedia. When it comes to the finite volume method, I'm not aware of any similarly ...
1
vote
1answer
112 views
FFT Poisson Solver for non-uniform grid
I have a 3D solver for the incompressible Navier-Stokes equations which uses a FFT library for the Poisson equation with a uniform grid on all directions. In 2D the Poisson equation is given by:
$$
...
2
votes
3answers
373 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 $\Delta x$:
$$ \frac{\partial \rho}{\partial t} + u \...
1
vote
0answers
74 views
(Approximate) Incremental Projection Method for Navier-Stokes equations
I am trying to implement an incremental projection method for the 2D incompressible Navier-Stokes. The type of projection method I am trying is
$$
\frac{u^{*} - u^{n}}{dt} = - \nabla p^{n} - u \cdot ...
0
votes
1answer
333 views
Proper boundary conditions for potential flow around cylinder
I am computing the stationary, incompressible, inviscid and irrotational flow around a circular cylinder using a discretization in general coordinates.
I derived a PDE and proper boundary conditions ...
1
vote
1answer
87 views
Simulating Stokes flow with an obstacle
I was asked to compute the Stokes flow (i.e. a low Reynolds fluid) near and obstacle. This is the first time I face a fluid and I am lost. What reference/general ideas/big theorems can you recommend ...
2
votes
1answer
81 views
Computational Fluid Dynamics: Question on a third-order accurate finite difference approximation
According to this paper the following finite difference approximation is third-order accurate:
$$\frac{d\rho_j}{dx}\approx\frac{2-\eta}{3}\frac{\rho_{j+1/2}-\rho_{j-1/2}}{\Delta x}+\frac{1+\eta}{3}\...
1
vote
0answers
55 views
Vortex Lattice Method: better basis than horse-shoe vortex?
I read several introductory texts about potential flow and vortex lattice method. Basically, it is fitting of some velocity field described by conditions on velocity at some control points using basis ...
5
votes
3answers
218 views
How can I make sure the flow is divergence-free when I use moving mesh?
I am using projection method and P2/P1 finite element method to solve the incompressible Navier-Stokes equations while the mesh is constantly adapted as the body moves (edge swapping, splitting and ...
1
vote
0answers
77 views
Computational approaches to analyse numerical solutions
I apologise beforehand if the question isn't well defined or is too broad, I'm just having some difficulty finding the information I need. I also apologise if this should have been asked on stack ...
6
votes
1answer
139 views
Pressure definition/convergence issues for the Incompressible Navier-Stokes when using a stabilized P1-P1 finite element formulation
I believe this might be a recurring topic, but i have not found a post that directly related to this issue.
I come from a finite volume background and my experience is more with predictor-corrector ...
