software

Introduction

It has been almost a year since Ubuntu 24.04 LTS Noble Numbat was released. Since it seems to be stable enough, I decided to migrate from 22.04 to 24.04 with a clean install.

I usually installed from the Japanese Remix ISO image, but since this version Japanese Remix is not released, I downloaded the image from Canonical’s page and installed it.

Introduction

Two months ago in this post, laminar flow around a 2D circular cylinder (Laminar Flow), using the governing equations for each of the ST and VP forms, The simulation was performed using the governing equations for each of the ST form and VP form.

Since then, we have simulated the flow around a 2-D cylinder in the time range 0 to 60 seconds for various parameters, and the results are summarized here.

Motivation

I have been studying PINNs and related OpenFOAM for a while, but yesterday there was a big news in LLM area and I decided to use Deep Seek-R1 which had an impact not only on LLM area but also on stock prices. Since I could not use it as it is in my environment, I used a compacted LLM with quantization.

This time, I used Ollama and Open WebUI to use the quantized model from a browser, and I will summarize the contents.

Introduction

As mentioned in a recent posting, I am conducting a tutorial on flow around a 2-dimensional cylinder. While conducting this tutorial, I was unable to use pyFoamPlotWatcher.py and gnuplot in my environment. In this post, I summarize how to improve them.

Motivation

Since the end of last year, I have been studying PINNs, learning models using the PINNs method for 2-dimensional fluids, and using those models to make inferences. It was not easy to show the results of the paper I referred to, and I had some difficulties. As I wrote in the “Summary” section of this post, I was thinking of trying to predict the Karman’s vortex street using the PINNs method.

In the course of my research, I learned from this paper that “data-free PINNs are unable to predict vortex shedding”. If that is the case, I decided to try simulating the Karman’s vortex in OpenFOAM first.

This post is a summary of my simulation of the Karman’s vortex in OpenFOAM.

Introduction

In my previous post, I summarized the learning and inference results from PINNs for Laminar Flow (laminar flow) in the unsteady state, using the governing equations of ST (Stress Tensor) form. The results were different from those in the referenced paper.

Introduction.

In previous post, I reproduced the Laminar Flow of the transition state in PINNs using the governing equations of the VP form with reference to the paper, but the results were very different from the values in the reference paper. This time, I also performed it with the governing equations of ST form, and I will summarize the results in this post.

Introduction

I recently posted what was obtained by PINNs for steady-state laminar flow. This time, I applied the PINNs method to unsteady laminar flows. The results of this time are not correct and different from the results of the referenced paper. I am investigating the cause, but I do not know.

Introduction

I have been trying to simulate steady state laminar flows with PINNs since the end of last year, but I was stumped by the derivation of the Navier Stokes (NS) equations of Cauchy stress tensor type. I coded PINNs with the governing equations based on the Velocity-pressure type NS equations. I got a result that looks like it, and I will summarize it in this post.

Introduction

Continuing from yesterday, I tried the book example (Chapter 4 of the book). It was quite interesting.