# Questions tagged [fluid-dynamics]

The study of the properties of fluids and gases in motion

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### 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 ...
655 views

### 1-D incompressible unsteady Couette Flow Explicit finite differece CFD

I am currently following J.Anderson Jr.'s CFD with basic application and I came into some troubles while coding for my very first CFD problem. As the title suggests I am solving an incompressible ...
46 views

### Shallow water equations with moving body

I was wondering if there are any shallow water equation solvers out there that can include rigid body motion for the surface the water flows on?
356 views

### Rhie and Chow Pressure Velocity Coupling

In a collocated grid, which velocity is used in the convective term in the momentum equation? Is the Rhie and Chow constructed face velocity or an average of the adjacent cell center values(in a ...
486 views

### CFL condition in Discontinuous Galerkin schemes

I have implemented an ADER-Discontinuous Galerkin scheme for the resolution of linear systems of conservation laws of the type of $\partial_t U + A \partial_x U + B \partial_y U=0$ and observed that ...
99 views

### Order of local and global truncation error in a finite volume scheme

Can the order of the local truncation error be higher than the order of global truncation error in a finite volume method?
487 views

### Finite volume a posteriori error estimation

I'm wondering what alternatives there are to a grid convergence study to judge solution accuracy for a given grid resolution when doing steady-state RANS simulations on an automatically generated ...
698 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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### A stable method for solving monontoe HJB equation

I am considering solving HJB equation of the form $$v_t=g(a(x)v_x),\quad x\in \mathbb{R}, t>0,$$ with initial condition $v(0)=v_0$. Here $g:\mathbb{R}\to \mathbb{R}$ is Lipschitz and monotone ...
753 views

### Simple methods for solving 2D steady incompressible flow?

I'm trying to make a CFD model where I can place a source and a sink anywhere in a grid and get the fluid flow rate across each cell boundary between those locations. I'm starting simple with a 3x3 ...
122 views

### How one could choose the value of viscous coefficient for obtaining stable solution of Burgers' equation?

Burgers' equation is a fundamental PDE used in various fields such as number theory, gas dynamics, heat conduction, elasticity, etc. It is crucial especially for developing numerical models for ...
220 views

### Implicit integration for FLIP?

I have problem with volume loss in FLIP simulation. Unfortunately it's necessary to obey the CFL condition when using explicit integration methods (RK2 in my case) to advance particle positions using ...
45 views

### Number of particles that could be used in a simulation

For a computer with 8 GB of memory, which is the order of magnitude for the number of particles that could be used in a simulation. Is the answer $N=8/6\times 10^9$? or do the particles take up more ...
918 views

### How to choose the relaxation time in the Lattice Boltzmann Method?

We know that the relaxation time is very important in LBM. I have searched lost of papers, but can't find some systematic introductions about the choice of relaxation time in SRT LBM. Could you give ...
138 views

### Stability of the explicit MacCormack Scheme to solve the Navier Stokes equations with Wilcox's K-Omega Turbulence Model

I am solving turbulent pipe flow with an explicit MacCormack scheme and Wilcox k-omega model. The laminar version of the code had three distinct stability criteria which worked fine after ...
184 views

### Flow past square cylinder benchmark in 2D. Famous papers to compare

I'm looking for a benchmark for the flow past square cylinder problem in 2D to compare my results. I have found some papers, but it seems that there are different results in different papers. I want ...
238 views

### How can an engineering student become a computational scinece expert in a short time [closed]

How can a student with zero computing or programming language knowledge, few engineering mathematics knowledge, understand computational science especially Finite Element Modelling (FEM) from ...
199 views

### Benchmark setup for incompressible Rayleigh-Taylor flow

I'm trying to benchmark a new numerical method for the incompressible Navier-Stokes equations. I'd like to use the most widely-accepted test cases possible. In particular, I'm looking for a ...
274 views

### Algorithm for face based data-structure - CFD

Good morning I'm trying to develop an unstructured CFD code to solve Euler equations in a finite-volume (cell-centered) context (learning purposes). I was able to build from a cgns file some basic ...
2k views

### Is there an advantage of using a staggered grid over a regular one when combined with high order methods?

The title says is all. This question is in the contest of an incompressible Navier-Stokes solver. Specifically, I am currently working on a new solver while referring myself to an older code for ...
364 views

### Outlet boundary condisions in lattice Boltzmann Method

Here is the flow past a square cylinder configuration. The problem is a viscous and incompressible with parabolic velocity profile using freestream velocity U across single cylinder. I use the single ...
100 views

### What is a good algorithm to solve a discrete continuity equation in Cylindrical coordinates?

The equation is: $\partial f/\partial t + \nabla \cdot (v f) = 0$ $, \;\; f \in [0,1]$ and $v$ is a velocity known at every grid cell. A more precise constraint is that $f$ is either 0 or 1 but ...
10k views

### The real myth of GPU (specifically CUDA) really speed up FEM/CFD

Now I have been believing that FEM/CFD is supposed to be faster on a GPU unit - here I am using CUDA as solid example. However, I have not been able to find a convincing paper where the benchmark ...
555 views

### Discrete conservation and Finite Element methods

What would be the rigorous mathematical expression of the fact that a conservation law discretized with a Finite Element method with Galerkin discretization does not result in a conservative scheme ?
113 views

### How to discretize the surface of a prolate spheroid?

I need to discretize the surface of prolate spheroid given by the equation $$\frac{x^2}{L^2} + \frac{y^2}{D^2} + \frac{z^2}{D^2} = \frac{1}{4}$$ The surface has to be divided to 500 equal panels to ...
263 views

### Pressure-Pressure BC

My FDM code simulates Backward Facing Step flow when I use conventional BCs such as defining velocity profile at inlet and fully developed condition at outlet. I have validated the results and it ...
68 views

### Cavity Flow CFD Boundary conditions and strange waves

So I have a PDE that I use to describe how material flows through a volume(2D or 3D). $$\frac{\partial C}{\partial t} + \vec{u} \cdot \nabla C = (D' + D )\nabla^2C$$ Now using finite differences I get ...
352 views

### Difficult bug in my 2D Compressible Euler solver

For the past few days, I have been writing a numerical solver for the 2D compressible Euler equations for an ideal gas. My numerical method has been the Local Lax Friedrichs or "Rusanov's method." ...
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