Questions tagged [fluid-dynamics]

The study of the properties of fluids and gases in motion

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Specifying boundary conditions for imported mesh in OpenFOAM

I have a mesh produced from scanning a real 3D object (I don't have a geometry). What is the most convenient way to specify inlets, outlets, etc. for CFD in OpenFOAM? The mesh consists of thousands of ...
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2answers
151 views

Which tool/metric do you recommend to evaluate the quality and validity of a Large Eddy Simulation?

The idea behind Large Eddy Simulation is to solve explicitely the scales of the flow that are resolved by the computational grid and to model the sub-grid scales. Ideally, the cut-off between these ...
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2answers
3k views

Recovering pressure from velocity or streamfunction fields

I am interested in 2D channel flow of an incompressible Stokes fluid (Re << 1), with periodic boundary conditions in the x-direction and no-slip at the walls in the y-direction. I have existing ...
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2answers
858 views

A Question About the Rhie-Chow Interpolation Used for Solving the Incompressible Navier-Stokes Equations on Unstructured Grids

When using the SIMPLE method on a mesh with a collocated variable arrangement, the following interpolation is used for the advecting velocities: \begin{equation} u_f = \overline{u}_f - \overline{D}_f\...
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3answers
453 views

Variable viscosity Stokes equation

One very efficient way to solve Stokes equation with periodic boundary conditions \begin{equation} -\eta \nabla^{2} \bf{v} + \nabla p = f \\ \nabla \cdot \bf{v} = 0 \end{equation} is using the ...
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2answers
524 views

Reference request for computational fluid dynamics

I have good background of finite element methods and continuum mechanics and I am familiar with fluid mechanics. My aim is to understand the required theory and to write my own simple codes using ...
5
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1answer
262 views

Is there a jump condition for this PDE? ( Brinkman model , piecewise constant permeability)

The Brinkman equations for steady flow of an incompressible fluid through rigid porous solid are: $-\dfrac{\mu_0}{k}\mathbf{v} - \mathrm{grad}p + \mu_0 \Delta \mathbf{v} =0$ and $\mathrm{div}(\mathbf{...
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4answers
836 views

What methods exist to solve for the fluid flow past a cylinder using finite differences on a Cartesian grid?

I'm interested in finite-difference approaches to the incompressible Navier-Stokes equations that can handle complex geometry without the use of an unstructured mesh or a non-Cartesian grid. To be ...
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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 ...
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Is it generally unstable to use in multidimensional simulations finite difference schemes with higher orders than 2?

I'm part of a team trying to generalize a 1D Advection-Diffussion-Reaction code we inherited by extending it to 2D by using dimensional splitting, i.e. solving advection and diffusion for x and y ...
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237 views

Negative viscosity stabilized by fourth order terms

I am trying to solve a "Navier-Stokes"-type problem where the viscosity is negative. Of course this renders the equation unstable and thus I add a fourth order term, so the entire equation becomes: $$...
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What are the governing equations solved in coupled atmosphere-ocean models?

In (hydrostatic) atmospheric general circulation models, for example the so-calle Primitive Equations, consisting of the horizontal momentum equation, the hydrostatic balance, the continuity equation, ...
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973 views

How does GAMG in OpenFOAM really work?

I use OpenFOAM for CFD simulations. A very popular preconditioner is GAMG which needs a low number of iterations per a time step in SIMPLE or PISO solvers that are used to simulate the fluid flow. I ...
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4answers
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Practical coding resources for new CFD practicioners

There seem to be many books and papers that explain various CFD methods in great detail, but unfortunately I have not been able to find many good resources of such methods implemented in codes such as ...
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1answer
154 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 ...
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2answers
461 views

Poiseuille flow

I have probably a very stupid problem. I can't solve a simple Poiseuille flow in a straight 2-D channel driven by a pressure drop. Results are complete nonsense. (Setting zero pressure on the outflow ...
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4answers
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How to deal with nonlinear term in Navier Stokes equations (finite element code)

I am trying to solve the Navier Stokes equations using the finite element method. I plan on using the pressure correction method to deal with the pressure and an implicit time stepping scheme for ...
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2answers
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Software for 3D Navier-Stokes equation

What is the best software for solving and simulating the 3D Navier-Stokes equation for incompressible laminar non-Newtonian fluid flow?
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How to discretize Burger's equation?

I am trying to solve the very simple one dimensional burgers equation which is: $$\frac{\delta U}{\delta t} + \frac{\delta F}{\delta x} = 0$$ where the flux F of some variable U is defined as$$ F= \...
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3answers
229 views

vector PDEs on manifolds

What are the subtleties involved in solving vector PDEs on manifolds? Can someone suggest a reference summarizing the problems involved? Specifically I want to solve a vector Helmholtz equation with ...
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2answers
160 views

Why does the wrong mesh scale produce a more accurate result?

I am using an Euler-Euler method to model two phases - both are treated as a continuum using modified Navier-Stokes equations. One phase is air and the other is particles, that are being entrained by ...
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3answers
162 views

nuclear reaction fluid modelling

I'm pretty ignorant regarding the dark arts of numerical codes and modelling, but i'm interested in trying to pursue it for a particular pet project. It regards modelling of nuclear reactions like ...
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2answers
490 views

How are Spectral Methods applied to CFD? In particular, how is the pressure-velocity coupling implemented?

I know that spectral-methods which are weighted-residual methods can be applied to solve for the incompressible N-S equations. In particular, they are applied to Direct Numerical Simulations (DNS) for ...
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1answer
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Is stabilization of energy equation needed when momentum equation needs it?

When SUPG/PSPG stabilization is added to momentum equation of flow problem, is needed stabilization for energy equation also? I would guess that when stabilization for velocity works fine so one gets ...
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1answer
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Effecient CFD programming techniques

I'm trying to make highly efficient CFD programming complex for solving combustion problems. I've finished writing core which realises mathematical model, and now I'm concerned about code performance. ...
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1answer
663 views

Continuous vs discontinuous pressure elements in fluid flow problems

When solving fluid flow problems using finite elements you typically end up requiring that $p\in L^2$. For Darcy flow problems, a popular choice of elements is the Raviart-Thomas element and ...
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1answer
335 views

Finite Elements Weak Formulation generalization

I am struggling with an equation that represents the Weak form of Galerkin method: $ \phi^{T}F(\textbf{u})\sim \int_{\Omega}^{ } \phi.f_{0}(\mathit{u},\nabla \mathit{u}) + \nabla\phi:f_{1}(\mathit{u},...
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1answer
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Properties of a Shockwave in Fluid Calculations

The comments on the accepted answer of my previous question here have left me with a more general question about accurately capturing shockwaves in fluid calculations. For the sake of having an ...
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1answer
104 views

Modelling flow through pipe networks

I'm trying to educate myself on modelling solute flows through pipe networks. This is a follow up of my previous post here $$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$ While ...
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2answers
238 views

Preconditioner for the GMRES method in the Uzawa algorithm

I'm trying to solve \begin{equation}\left\{ \begin{split} \frac{\partial u}{\partial t}+(u\cdot\nabla)u-\nu\Delta u+\frac1\rho\nabla p&=f\;\;\;\text{in }\Lambda\\ u&=0\;\;\;\text{on }\partial\...
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2answers
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Projection Method: Boundary condition on intermediate velocity field

I'm trying to solve variable density and viscosity Navier-Stokes equation using lagged pressure projection method. I'm solving for cavity problem as a test case now (once I get projection right, I ...
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2answers
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CFD: multiphase flow modeling of a laminar flow reactor

I am planning to model the laminar flow reactor shown in the picture below using computational fluid dynamics (CFD). The laminar flow reactor is used to study a multiphase flow: a layer of sheath air ...
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2answers
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Finite volume discretization of non-conservative linear hyperbolic equation

Problem. Consider the one-dimensional adjoint Euler equations for $(x,t) \in \Omega \times [0,T]$ with $\Omega \subset \mathbb{R}$ and $T > 0$ $$ \varphi_t + \Big(\frac{\mathrm{d}F}{\mathrm{d} U}(x)...
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1answer
285 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 ...
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2answers
557 views

Time discretization: Runge-Kutta methods vs. standard backward difference

I've recently written a code that solves the incompressible/low-Mach number formulation of the Navier-Stokes equation with high-order methods for both time and space. My advisor insisted that I use ...
4
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1answer
381 views

Fast Multipole Method in 3D

I am writing a FMM (Fast Multipole Method) algorithm in 3D. I generated the mesh and, currently, I am developing the expansion and the three (M2M, M2L, L2L) translation operators using spherical ...
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2answers
561 views

Manufactured solution for pressure based 3d incompressible Navier-Stokes solver with wall boundaries

I already successfully verified my solver (SIMPLE-type FVM-method) with the following manufactured solution (3d Taylor-Green vortex) on the solution domain $[-1,1]^3$ with Dirichlet boundary ...
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1answer
99 views

Zero-k mode in Pseudo-spectral solution of Stokes Flow

I'm trying to solve a Stokes flow problem with a pseudo-spectral method in periodic boundary conditions. The equations of interest are $-\nabla^2 \bf{v} + \nabla p = \bf{f} \\ \nabla \cdot \bf{v} = ...
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1answer
589 views

Organizing a CFD program written in python

I've spent some time writing a spectral element solver aimed at solving fluid flow problems concerning the motion of self-propelled bodies. I've gotten to the point where the code has grown long ...
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1answer
2k views

Comparison of Lattice Boltzmann Method vs Traditional Navier-Stokes based Methods

I have a choice of two options, analysing and implementing Lattice Boltzmann methods or traditional Navier Stokes based methods. I'm a CFD newbie and I have a rough idea (though not rigorous enough to ...
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1answer
2k views

calculation time in Fluent

I'm making a model of a square box where water comes in and the water level rises. I want it to be a transient, turbulent, VOF-model. The velocity of water entering changes in time ($-0.2$ to $0.2$ m/...
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2answers
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4th order Padé scheme formula derivation

I am trying to derive the formula of the 4th order Padé scheme that passes through the points $x_i$, $x_{i-1}$ and $x_{i+1}$ $$\Big(\frac{\partial\phi}{\partial x} \Big)_i = -\frac{1}{4}\Big(\frac{\...
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1answer
151 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 ...
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1answer
210 views

Generalized Eigenvalue Problem from linear stability analysis

I also posted this in the physics forum, but maybe here it fits better. I am trying to solve a generalized eigenvalue problem raised by linear stability analysis $$AV=\lambda BV.$$ $A$ and $B$ are ...
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1answer
337 views

OpenFOAM precipitation/crystallisation reaction solver

This question is probably related to chemical engineers that are around this forum. I am looking into writing a solver for a precipitation reaction (struvite to be precise): A+B+C+D <=> E+F A, B, ...
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1answer
136 views

transverse component for multidimensional advection in method of lines

So I inherited from some people a code that solves the advection-diffusion-reaction equation for a particular system. The original code was first implemented in 1D which worked fine in cartesian ...
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909 views

How to implement boundary conditions on Finite Difference WENO5 scheme for the Euler equations

I'm implementing a Finite Difference WENO5 with Lax-Friedrich flux splitting on a uniform, structured grid to solve the 2D Euler equations of fluid dynamics on a rectangular domain in cartesian ...
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How does one handle the source term in the Shallow Water Equations when using the discontinuous galerkin method? [closed]

I use the discontinuous galerkin method to solve the steady flow 1D shallow water equations with a bump at the bottom. This flow is frictionless. I use the runge-kutta method to approximate the time ...
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4answers
10k views

Estimating the Courant number for the Navier-Stokes Equations under differing Reynolds number regimes

I am familiar with the Courant-Friedrich-Lewy Condition in as far as it applies to the stability of explicit finite difference schemes for standard parabolic and hyperbolic PDEs. However, when ...
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2answers
131 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 ...

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