akenji's lab

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.

Introduction

Yesterday, I installed OpenFOAM and ParaView and tried to simulate and visualize a Poiseuille flow (Hagen-poiseuille flow). This time, I followed the book and ran “cavity” from the OpenFOAM built-in tutorial.

Motivation

I have been working on PINNs since the end of last year and have attempted two problems. I am planning to select and work on problems in the field of fluid dynamics. In fact, I am working on incompressible flow around a cylinder, but I have been stuck for a week because I can’t figure out how to relate the output of the model to the differential equations (the key part of PINNs).

I decided to learn a bit of OpenFOAM if I am going to work on the fluid dynamics area, so I installed OpenFOAM, ParaView, and tried the examples.