Questions tagged [fluid-dynamics]
The study of the properties of fluids and gases in motion
544
questions
3
votes
1answer
122 views
Time discretization Navier Stokes equation
This question is a follow-up of this one.
The weak form of Navier Stokes equation is (assuming $v,q$ test functions for the velocity and the pressure, respectively)
$$(\frac{du}{dt},v)_{\Omega} + (\...
1
vote
0answers
48 views
How to numerically solve PDE that governs the free vortex wake model?
Crossposted at Math SE
I am reading a paper on the free vortex wake model for a helicopter rotor blade, which is described by the following PDE:
$$\frac{\partial \vec{r}}{\partial \psi} (\psi, \zeta) ...
0
votes
0answers
50 views
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 ...
1
vote
0answers
54 views
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 ...
3
votes
1answer
70 views
Why do we have to resort to Higher order schemes for solving the 1-D advection equation/ continuity equation?
\begin{equation}
\begin{aligned}
\frac{\partial N}{\partial t} &+ \frac{\partial J}{\partial r} = 0, \\
\frac{\partial N}{\partial t} &+ \frac{\partial }{\partial r}(N \upsilon ...
0
votes
0answers
35 views
Insert a boundary condition without removing periodicity assumption
I've to perform a multi-fluid internal flow simulation with a code which intrinsically assumes periodicity on a given direction (say z) on a cartesian grid. Nonetheless, the problem I'm trying to ...
-3
votes
1answer
78 views
How to avoid negative concentration from numerical solution using FDM scheme?
$\frac{\partial C}{\partial t} + u \frac{\partial C}{\partial x} + w \frac{\partial C}{\partial x} = D \left(\frac{\partial^2C}{\partial x^2}+\frac{\partial^2C}{\partial y^2}\right)-C \cdot \left(\...
0
votes
0answers
88 views
Tool that calculates total drag for a submarine
Can you please suggest a tool (software or online tool) that can analyze a submarine hull shape and give the total drag at a specific velocity.
A simplified tool would work too, where I select a ...
3
votes
0answers
77 views
Galerkin Least-Squares stabilization for FEM solution advection (hyperbolic) equations
I am playing with Galerkin Least-Squares stabilization to solve advection diffusion problem in the context of the finite element method. This works very well for steady-state advection-diffusion ...
5
votes
1answer
138 views
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.
$$\frac{\partial u}{\partial t}+u(\nabla \cdot u)=-\frac{1}{\rho}\nabla p+\nabla ^2 u$$
...
3
votes
2answers
107 views
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 & ...
1
vote
0answers
47 views
What exactly are WENO schemes and where are they used?
I am currently trying to understand what WENO schemes are and most of the literature on web talks about cell-face reconstruction. What I am unable to understand is the origin of these discontinuities ...
1
vote
0answers
83 views
Advection equation boundary conditions in 2D unstructured grid
Currently struggling with boundary conditions for 2d advection equation.
left dirichlet u = (1,0)
bot top dirichlet u = (0,0)
right neumann du/dx = (0,0)
...
1
vote
0answers
87 views
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 ...
2
votes
0answers
48 views
What is temporal order of accuracy of the PISO algorithm?
A few Computational Fluid Dynamics (CFD) codes implement the so called PISO (Pressure-Implicit with Splitting of Operators) algorithm for pressure-velocity coupling.
My concern is what is actual ...
0
votes
3answers
134 views
How to apply the boundary condition when global stiffness matrix is stored in csr format? [duplicate]
I am solving the poisson equation and I constructed the global stiffness matrix in compressed row storage format. Then I wrote the preconditioned conjugate gradient solver for solving the system of ...
-1
votes
1answer
99 views
Implementation of Source Panel Method as Described in Katz Plotkin Book
I am currently trying to implement Source Panel method as described in Katz and Plotkin in Low Speed Aerodynamics. I have successfully implemented two previous methods. However, I am fully blocked on ...
0
votes
1answer
98 views
Unstructured mesh preprocessing
For solving PDE with self written code it is needed to preprocess the data from mesh generators. I recently started shifting from cartesian grid to unstructured.
I finished reading up to FVM part of ...
0
votes
0answers
43 views
Boundary layer and high order finite element methods
When modeling boundary layers, it is typically required to have a highly refined mesh along the boundary. My question is if there has been success with high order finite element methods to overcome ...
2
votes
0answers
84 views
How are finite volume method boundary conditions implemented without using ghost-cells?
I'm currently trying to implement my own FVM code in cpp, but when I try to calculate the laplacian of a test function, given by \begin{align}\phi_0=\sin(2\pi x)\sin(2\pi y)\end{align}, I get ...
0
votes
1answer
121 views
L2 projection with bounds
In some problems we are currently working on, we are working with discontinuous functions that are defined on a finite element mesh and are established using Lagrangian particles. To obtain them on a ...
0
votes
0answers
49 views
Simulating a combustion process
I want to try simulation-(and not experimental)-driven approach to design custom fireplace fuel burners.
What software applications, libraries, code and model templates can I use to model and ...
0
votes
0answers
44 views
When to stop iterations in SOR solver for 3D Poisson equation
I'm writing a solver (in C) for 3D incompressible fluids, using the finite-differences method, and I'm finding a somewhat surprising behaviour: the solver provides "good-looking" solutions, ...
0
votes
0answers
24 views
How to define "Characteristic length in Ansys CFX Power Syntax script?
I am trying to evaluate Reynolds number in Ansys CFX 2020 R2 using CCL/Perl script on different domains in a radial turbine. But for that, I need to define the Characteristic length. So I define the ...
3
votes
1answer
67 views
How does the diffusion of a finite volume method with a WENO scheme compare with that of spectral methods?
I know that, in general, finite volume (FV) methods are more (numerically) diffusive than spectral methods. However, I can't find any information on how the advection scheme changes that.
For example, ...
0
votes
0answers
46 views
Unsteady Stokes equations in ALE framework
I'm trying to solve Unsteady Stokes equations on a moving domain, using an ALE formulation, that is
$$\frac{\partial \mathbf{u}}{\partial t} - \mathbf{w}\cdot \nabla\mathbf{u} = \nu\Delta\mathbf{u} - \...
1
vote
1answer
123 views
Is there any way to have a better guess for initial condition of an ODE coupled to CFD as a boundary condition?
I'm doing CFD simulations for blood flow in unstructured grids. My boundary condition at the outlets is called three-element Windkessel which basically calculates the pressure by solving this ODE:
$$...
3
votes
2answers
146 views
Why are fluid simulations so hard?
Fluid simulations solving the hydrodynamic (HD) or the magneto-hydrodynamic (MHD) equations are very useful in physics, the latter being particularly useful for modeling plasmas.
Of course these ...
0
votes
0answers
20 views
Probability Density Function of DNS velocity field [duplicate]
I am currently working on a DNS turbulent solver and I would like to compare my IHT simulations to papers. Those papers show the Probability Density Function of the velocity field:
I would like to ...
0
votes
1answer
63 views
Handling time derivative as source term in SDIRK methods
I am currently facing some challenge implementing a less traditional PDE which take a form similar to the Navier-Stokes equation, except that the continuity equation is modified such that:
$$\epsilon \...
3
votes
0answers
59 views
Is it possible to shift the numerical results in order to compare it with the analytical solution?
I'm using lattice Boltzmann method (LBM) to do simulation of flow in a pipe. The diameter of the pipe is 0.02 m and its height is 0.1 m. I put a parabolic velocity profile at the inlet:
$$\mathbf{u}(\...
0
votes
0answers
49 views
Finding a CFD paper with extra degree of freedom variable in mass conservation
I am trying to find a paper that I saw about a year ago. I am not sure of the actual date of the paper.
I believe it was a finite difference CFD paper. The interesting part of the paper was the ...
1
vote
1answer
90 views
Imposing pressure variation instead of Dirichlet boundary conditions on Finite Element Method
I always see Finite Element codes solving PDE with Dirichlet or Neumann boundary conditions. But, I have a problem now consisting of a straight cylinder with a circular base (a simple 3D tube), with ...
2
votes
1answer
60 views
Understading memory sharing in a GPGPU using a lattice example
I am new in the GPUs world, I used them in Matlab ambient so I didn't need to appreciate the subtleties of these devices.
I know that a GPU can be divided into multiprocessors (also called Streaming ...
0
votes
0answers
159 views
How to calculate the average velocity over a surface through time using paraview?
My problem is a little more complex, but here is a simplified similar model.
Let us consider a fire source inside a box and the hot gases (burnt or unburnt) from the combustion are going out of the ...
0
votes
0answers
40 views
Effect of Peclet number on concentration profiles
I have been performing convection-diffusion transport studies on microfluidic channels like the following
I came across an article that illustrates the effect fo Peclet number on concentration ...
1
vote
0answers
55 views
computing time scale and steady state concentration in microfluidic channels
I have been performing convection-diffusion transport studies on microfluidic channels like the following
The inlet concentration is specific and I obtain the time-dependent concentration profiles of ...
1
vote
1answer
84 views
Would modeling a fluid flow that decreases in magnitude violate conservation of mass?
If I make a quasi-steady assumption in a model such as keeping the fluid density constant and assuming the flow is incompressible, does modeling a flow with decreasing velocity / magnitude, say, as ...
1
vote
0answers
48 views
Understanding STRUCTURED_POINTS dataset in VTK
Based on my readings this is what I have gathered:
Dimensions: Number of data points in the x, y, z directions
Spacing: Space between points in each dimension
Origin: Location of origin
Cell data: ...
0
votes
2answers
65 views
Grid Independence Study
Is the change in time step necessary for the grid independent study? As the CFL is based on the relation between dt and dx.
In mesh independent study, only change should be mesh i.e, dx isn't it so?
0
votes
1answer
97 views
Extracting data from VTK simulations using C++
I have been given a few numerical simulations regarding fluid mixing and have been asked to extract a few parameters from them using C++. Altogether there are about 1000 VTK files per simulation, and ...
1
vote
1answer
266 views
DNS simulation in industry
I have this idea in my mind that Direct Numerical Simulation (DNS) is only used in research since the Reynolds numbers of industrial applications are too high and require computer horsepower we don't ...
2
votes
1answer
90 views
Is the Immersed Boundary (IB) method a Direct Numerical Simulation?
Is the Immersed Boundary (IB) method considered a Direct Numerical Simulation?
A DNS code is the most detailed type of simulation and the most accurate but computationally expensive, right?
What makes ...
1
vote
1answer
356 views
Reading VTK file into C++ for analysis
I apologize in advance if this post is at all ignorant or elementary, I am a pure mathematician who is newly getting into the world of scientific computing.
For my research, my advisor would like me ...
3
votes
0answers
60 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,...
0
votes
1answer
113 views
Getting streamline for a lid driven cavity flow in openFoam/ParaView
I have installed openFoam on Debian GNU/Linux and learning from official user guide. I have a problem with generating streamlines. I am trying to generate streamlines as explained in the post ...
3
votes
0answers
91 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 ...
1
vote
0answers
27 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:
$$
\partial_t ...
0
votes
0answers
76 views
Numerical scheme to calculate the normal mode of a set of hyperbolic PDEs?
I would like to solve the linearised, ideal, MHD equations, where the gas pressure is zero.
$$\frac{\partial u_x}{\partial t}=v_A^2(x,z)\left[\nabla_{||}b_x - \frac{\partial b_{||}}{\partial x}\right],...
4
votes
1answer
205 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 ...
