Questions tagged [fluid-dynamics]

The study of the properties of fluids and gases in motion

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14 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 ...
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1answer
73 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 ...
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1answer
57 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 ...
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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{ ...
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23 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 ...
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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) ...
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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{...
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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-...
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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: ...
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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,...
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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 ...
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2answers
132 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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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(\...
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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 <...
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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 ...
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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 ...
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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}...
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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 ...
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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: ...
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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 ...
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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. ...
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1answer
175 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^...
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1answer
195 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} + (\...
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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) ...
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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 ...
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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 ...
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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 ...
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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 ...
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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(\...
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174 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 ...
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88 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 ...
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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. $$\frac{\partial u}{\partial t}+u(\nabla \cdot u)=-\frac{1}{\rho}\nabla p+\nabla ^2 u$$ ...
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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 & ...
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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 ...
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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 ...
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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 ...
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3answers
279 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 ...
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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 ...
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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 ...
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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 ...
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153 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 ...
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1answer
206 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 ...
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56 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 ...
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58 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, ...
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1answer
79 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, ...

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