All Questions
Tagged with finite-difference navier-stokes
25
questions
1
vote
1
answer
62
views
How to calculate the force of solid applied by fluid? Using finite difference method, DNS, staggered grid, SIMPLE algorithm, immersive boundary
Problem
I am using finite difference method to solve classic problem of flow around cylinder, for validation of my group's immersive boundary method.
The common way to validate numerical method is ...
- 31
0
votes
1
answer
46
views
How to address the element face adjacent to boundaries when the finite difference method and marker-and-cell scheme are used to solve the Stokes flow?
The Stokes equations are
$$-\Delta \mathbf u + \nabla p = f \text{, in }\Omega,$$ and
$$ -\nabla \cdot \mathbf u = g, \text{ in } \Omega$$
where $\mathbf u = \left( u, v \right)$ is the flow ...
- 323
1
vote
0
answers
62
views
Good non oscilliatory derivatives for an exsisting grid
I'm calculating the entropy production of a shockwave by utilizing the equations:
\begin{equation}
\sigma = J'_q\frac{\partial}{\partial x}\left(\frac{1}{T}\right) +\frac{1}{T}\frac{4\eta}{3}\left(\...
- 55
2
votes
1
answer
105
views
Fix for FD WENO method for multi-component compressible flows
I'm solving two-dimensional four-component compressible Navier-Stokes equations with finite-difference WENO approach. The equations are pretty standard:
$$
\frac{\partial U}{\partial t} +
\frac{\...
- 347
1
vote
2
answers
474
views
How to apply central difference to viscous fluxes in 2D Navier-Stokes equations?
I'm trying to solve 2D unsteady compressible Navier-Stokes equations with finite-difference or finite-volume method. Here is the system, it's pretty standard:
$$
\frac{\partial U}{\partial t} +
\frac{...
- 347
2
votes
0
answers
79
views
Haw to apply central difference to viscous flux in energy equation?
In many modern papers Navier-Stokes equations are solved with finite-difference or finite-volume methods using WENO reconstruction for non-viscous fluxes and central differences for viscous ones. It ...
- 347
2
votes
2
answers
171
views
Simplest way to "upgrade" from Euler equations to Navier-Stokes equations in FV or FD framework
I have quite a lot of experience solving unsteady Euler equations, including multi-component ones, with in house-coded finite-difference and finite-volume methods, including MacCormack and MUSCLE ...
- 347
0
votes
1
answer
187
views
FDM on nonlinear PDEs
I'm working with a 2D Navier Stokes PDE in the unstabilized version - the equation is a linear equation of the type $\frac{∂u}{∂t} = F(u,t)$.
In order to perform time discretization with FDM (finite ...
1
vote
0
answers
109
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Pressure boundary conditions in Stokes Equation in 2D
I am solving the steady-state incompressible Stokes equations in 2D:
\begin{equation}
\frac{\partial u_x}{\partial x} + \frac{\partial u_y}{\partial y} = 0,
\end{equation}
\begin{equation}
\mu\left[\...
- 31
4
votes
3
answers
4k
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 ...
- 161
0
votes
0
answers
229
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Double mach reflection at a inclined wedge
I am running into a strange problem when solving the 2D compressible Euler equations on a inclined wedge. To elaborate, my top boundary condition seems to emitting some type of instability. I have ...
- 75
3
votes
0
answers
95
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Solving numerically a linearized system of elliptic (?) Navier-Stokes equation (Shallow Water Derived)
For my PhD Thesis, my advisor asked me to build a solver inspired from the article "Optimal Control Theory Applied to an Objective Analysis of a Tidal Current Mapping by HF Radar, J-L Devenon, 1989". ...
- 31
1
vote
1
answer
2k
views
How to implement finite difference method for one dimensional Navier-Stokes PDEs
I am trying to use backwards finite difference method to numerically solve a pair of partial differential equations:
$\frac{\partial \left(pv\right)}{\partial x}+\frac{\partial p}{\partial t}=0$
$\...
- 147
0
votes
1
answer
1k
views
Interpolation of velocities on staggered grid (in PIC)
Edit: (copying from my comment)
Let's consider the inverse problem when I need to transfer velocities from particles to the grid (inverse bilinear interpolation). How'd I transfer a particle's x-...
- 185
1
vote
1
answer
606
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Upwind difference for velocity in staggered grid
I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf
In the paper, the nonlinear term is treated as mix of central central difference and upwind difference using a ...
- 203