Questions tagged [fluid-dynamics]
The study of the properties of fluids and gases in motion
570
questions
1
vote
0answers
21 views
Manufactured solution for advection diffusion equation
I am using the method of manufactured solutions to verify the implementation of a code.
My PDE is:
$$
\frac{\partial (T)}{\partial t} + \nabla \cdot ( \vec{v} T) - \frac{1}{\rho C_P} \nabla \cdot (k \...
-2
votes
0answers
23 views
Aeroacoustics Simulation in Star CCM+ using FW-H Model
Trying to simulate the aeroacoustics noise generation due to a flow over a open cavity using Broadband Noise Model and also noise propagation in the far field using FW-H Model.
The Star CCM user guide ...
1
vote
0answers
21 views
TVD slope / flux limiters formulation
Even if the formulation is the same the TVD slope limiter can be applied:
to state reconstruction at the interface, in 1D FV formulation, we reconstruct the $Q^*_{j+1/2}$ and the $Q^*_{j-1/2}$ in the ...
0
votes
1answer
75 views
Can I use periodic boundary conditions for `U` but not for `p`?
Cross-posted from Stack Overflow. (https://stackoverflow.com/questions/70686368/can-i-use-periodic-boundary-conditions-for-u-but-not-for-p)
I am trying to numerically compute the drag force around a ...
1
vote
1answer
60 views
Direct integration of 2D Euler Equations with Runge Kutta shows oscillating Courant-Friedrichs-Lewy coefficient. Stiff or Bug?
By writing the direct integration of the 2D Euler Equations in a wide and short box where the fluid enters and exits through the horizontal faces using the Runge Kutta O(4) method I have found that ...
2
votes
1answer
50 views
The effect of grid size on the total flux when solving Darcy flow with mixed finite element method
I am solving Darcy flow now with mixed finite element method. The Dary flow is
$$\begin{equation}\begin{aligned}k^{-1}\mathbf{q} + \nabla h=0, \text{ in } \Omega\\ %
\nabla\cdot \mathbf{q} = 0, \text{ ...
0
votes
0answers
24 views
Need help implementing constrained transport method for MHD riemann slver
I tried implementing constrained transport method to 1st order Godunov solver and when I run it on 2D rotor test case, the solver becomes unstable and crashed. The solver is able to maintain ...
1
vote
1answer
48 views
What are simple ways to simulate gas expansion from a pulsed nozzle into a vacuum?
I am doing a physics experiment that involves releasing gas from a reservoir into a vacuum chamber via a pulsed nozzle and I am interested in knowing what would be a simple (and reasonably accurate) ...
0
votes
1answer
75 views
Implementation of mixed hybrid finite element method
The mixed hybrid finite element method (MHFEM) is based on the mixed finite element method (MFEM). So, I'd recall the implementation of MFEM.
The mixed formulation of Poisson equation reads
$$\begin{...
2
votes
2answers
63 views
Possible to use Iterative FD methods to solve a transformed non square domain [matlab]?
For the 2-D Poisson equation $$-(u_{xx}+u_{yy}) = f \ \ \text{where} f = 1$$
For boundary conditions
$$\frac{\partial u}{\partial n} = 0 \ \text{on AB and AD}$$
$$ u = 0 \ \ \ \text{on BC and CD no-...
2
votes
1answer
94 views
Mineral dissolution and solute transport around a solid
I am trying to simulate solute transport of acid (HCl) and consequent mineral dissolution around a grain (calcite).
The governing equation for transport is the advection-diffusion equation, given as:
...
2
votes
1answer
100 views
Elementary matrix of Raviart-Thomas elements
We can use the $RT0$ to solve the Darcy equation, i.e.
$$k^{-1}\mathbf{u}+\nabla p = 0, \text{ in } \Omega,$$
$$-\nabla \cdot \mathbf{u} = 0, \text{ in } \Omega,$$
$$p = p_D \text{ on } \partial\Omega,...
3
votes
2answers
157 views
Test functions of Raviart-Thomas elements?
The test functions of general finite elements are like interpolation functions (if my understanding is correct). But how about test functions of Raviart-Thomas elements?
Let's raise the $RT0$ element ...
2
votes
2answers
133 views
What is the most suitable numerical approach for modelling multiphase flow with particle interactions?
If I want to build a solver for this following problem:
1. There is stagnant water governed by the Navier-Stokes equation in the domain.
...
2
votes
1answer
110 views
How to enforce fluid and solid dynamic coupling in fluid-structure interactions using the finite element method?
I apologize in advance if the question has been posted before or if it sounds a bit naive.
I am writing my own code in MATLAB for a staggered finite element solver for fluid-structure interaction ...
2
votes
1answer
64 views
Derivation of compressible volume-of-fluids formulation
I am trying to derivative the equations from [1] for a compressible Volume-of-fluids formulation but I am stuck in one of the last steps and would like to request some help to solve it.
The governing ...
2
votes
0answers
68 views
Solute transport around a solid obstacle
I am a newbie in CFD and single/multiphase flow and transport in general. As part of my quest to learn, I am trying to model solute transport around a solid object in the center of a 2D domain. The ...
3
votes
1answer
70 views
Instability at the boundary of a finite difference simulation of a hyperbolic PDE
I want to simulate the hyperbolic partial differential equation
$$W_{tt} + V W_{tx} + k_E V W_x + k W_t = 0,$$
but I am having trouble finding a discrete analog of this equation which is numerically ...
3
votes
1answer
108 views
Discontinuous pressure elements for incompressible Navier-Stokes
I am looking for some LBB-stable velocity-pressure combinations for incompressible Navier-Stokes where the pressure space is element-wise discontinuous, preferably with a linear variation elementwise. ...
1
vote
0answers
58 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(\...
3
votes
1answer
57 views
Jos Stam's stable fluids — why is the timestep multiplied by the number of grid cells?
One more question about Jos Stam's GDC tutorial on stable fluids: in the advection step on page 8, the timestep for each dimension is implemented as dt * N, where <...
1
vote
1answer
39 views
Jos Stam's stable fluids — why multiply by the grid size when subtracting out the curl-free part?
Considering page 10 of Jos Stam's GDC tutorial on stable fluids, the function project() first obtains the divergence of the velocity field: ¹
...
0
votes
1answer
89 views
Simulating the behavior of falling peas
I hope this is the right place for my question.
I am a university student who designed a pea-pouring machine.Now I‘m really interested in simulating the behavior of those peas.
Basically, they are ...
3
votes
1answer
88 views
Discretizing the viscous component in 1 - D Navier stokes compressive flow
I've been working on modelling the NS equations in order to simulate shock waves. The equations are set up on the form:
\begin{equation}
\frac{\partial U}{\partial t} + \frac{\partial F(U)}{\partial x}...
1
vote
1answer
145 views
Non-reflective boundary condition
I'm currently solving incompressible Navier-Stokes system of equations with periodic flow and high viscosity.
Is there any outlet boundary types that avoids the reflection of flow from the outlet back ...
2
votes
0answers
66 views
Multigrid method: linear solver and modified residual
I am trying to better understand the FAS multigrid algorithm for Euler equation in FV discretization. The usage of the modified residual (the residual with forcing) inside the different cases:
...
2
votes
2answers
80 views
Filter size of large eddy simulation with Smagorinsky sub-grid stress model
I am trying to implement Large eddy simulation for solving air flow simulation with large Reynolds number using Smagorinsky sub-grid stress model. I read that the filter size should be calculated ...
1
vote
0answers
98 views
Weird "oscillatory" modes appearing in FEM simulations
I am using COMSOL to solve a mathematical model involving thermoelectric hydrodynamic (TEMHD) flow. I am running a very large parameter sweep and using the solutions obtained to make some plots. ...
5
votes
1answer
177 views
Write incompressible Navier Stokes as ODE in $(\mathbf{u},p)$
Consider the Navier stokes equation after the discretization with conforming finite elements with source term $f=0$. We have the algebraic structure of a saddle point problem:
$$M \dot{u} = f- Au -B^...
3
votes
1answer
196 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)
$$(\frac{du}{dt},v)_{\Omega} + (\...
1
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0answers
50 views
How to numerically solve PDE that governs the free vortex wake model?
Crossposted at Math SE
I am reading a paper on the free vortex wake model for a helicopter rotor blade, which is described by the following PDE:
$$\frac{\partial \vec{r}}{\partial \psi} (\psi, \zeta) ...
0
votes
1answer
77 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
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0answers
55 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
82 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
36 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
80 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
176 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
89 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
180 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
124 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 & ...
2
votes
1answer
122 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
106 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
76 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
282 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
113 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
111 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
45 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
155 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
209 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
57 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 ...
