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📚 “An investment in knowledge pays the best interest.” – Benjamin Franklin

Apr 30, 2023

Hey friends & nerds! 👋

Welcome to the Sunday Science Newsletter where we explore science, systems & tools that help us become smarter scientists.

💦 But How DO Fluid Simulations Work?

Fluid simulations. How on is it possible that a computer can recreate the crashing waves, the rolling clouds and the swirling smoke that we see in our daily lives, phenomena which seem characterized by randomness and chaos? This video will attempt to explain exactly how the mathematics behind fluid simulations work.

💦 The Navier-Stokes Equations

In 1845, Sir George Stokes had derived the equation of motion of a viscous flow by adding Newtonian viscous terms, thereby the Navier-Stokes Equations had been brought to their final form which has been used to generate numerical solutions for fluid flow ever since.

In this equation, the formula for mass continuity is missing and other assumptions go into this equation. You can find the full derivation of the equation here.

🦴 Finite Element Method for Medicine

In this numerical method, a complex shape is divided into many small, simple geometries, such as cuboids.

The finite element method easily calculates the simple geometries' physical behavior. The individual simple geometries‘ results are then combined to recreate the physical behavior of the entire body.

Medical Simulation

📚 Can Physics-Informed Neural Networks beat the Finite Element Method?

TL;DR: “Considering the solution time and accuracy, PINNs are not able to beat the finite element method in our study.”

The recent success of deep neural networks at various approximation tasks has motivated their use in the numerical solution of PDEs. These so-called physics-informed neural networks and their variants have shown to be able to successfully approximate a large range of partial differential equations. So far, physics-informed neural networks and the finite element method have mainly been studied in isolation of each other.

Quanscient building a next generation Simulation-as-a-Service platform utilizing quantum computing and state-of-the-art algorithms.

They are working towards a future where hardware development is a breeze with automatic testing, simulations, and optimization happening behind the scenes.

Official Website

📚 Book of the Week

Data-Driven Fluid Mechanics: Combining First Principles and Machine Learning

This book presents an overview of some of the data-driven and machine learning tools that are leading research advancements in model-order reduction, system identification, flow control, and more.

Data-driven methods have become an essential part of the methodological portfolio of fluid dynamicists, motivating students and practitioners to gather practical knowledge from a diverse range of disciplines. These fields include computer science, statistics, optimization, signal processing, pattern recognition, nonlinear dynamics, and control.

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