Module 18 :Beyond Physics

Lecture One – Numerical Science, Mesh Concept & y⁺ Fundamentals This lecture introduces the fundamental numerical concepts behind CFD simulations, with a particular focus on mesh generation, boundary-layer resolution, and the importance of y⁺ in achieving accurate and reliable CFD results. Participants will understand how numerical discretization and near-wall mesh quality directly influence turbulence modelling, wall treatment, convergence, and solution accuracy. Key Topics & Skills Covered Numerical Science Fundamentals: Understand how governing equations are converted from continuous physical models into numerical solutions. Discretization Concepts: Introduction to Finite Volume, Finite Difference, and Finite Element methods. Mesh Fundamentals: Understand structured, unstructured, hybrid, and boundary-layer meshes. Mesh Quality: Study skewness, orthogonality, aspect ratio, non-orthogonal angle, and their impact on numerical stability. Boundary-Layer Theory: Understand the velocity profile and physical regions developing near solid walls. What is y⁺? Understand the dimensionless wall distance and its physical meaning in CFD. y⁺ Calculation: Learn how y⁺ is calculated from fluid properties, wall shear velocity, and the distance of the first cell from the wall. Turbulence Models & y⁺: Understand how the required y⁺ range depends on models such as k-ω SST, k-ε, RSM, and LES. Wall Treatment: Understand the difference between low-Re wall resolution and wall-function approaches. First Layer Height: Learn how to determine an appropriate first-layer height based on the desired y⁺. Inflation Layers: Understand how the number of layers, growth rate, and total inflation thickness affect boundary-layer resolution. y⁺ Control in ANSYS Fluent: Learn how to monitor and evaluate y⁺ distribution after running a simulation. y⁺ Distribution Analysis: Identify minimum, maximum, and area-weighted average y⁺ values and determine whether the mesh is appropriate. Mesh Independence: Understand why refining the mesh based on y⁺ and key engineering results is important for reliable simulations. Complex Geometries: Apply y⁺ concepts to curved walls, rotating machinery, airfoils, turbines, vehicles, and industrial equipment. Common Mistakes: Identify incorrect first-layer heights, inappropriate wall treatments, excessive growth rates, and non-uniform y⁺ distributions. CFD Best Practices: Develop a systematic approach for selecting mesh parameters and validating near-wall resolution. Professional CFD Workflow Physics & Turbulence Model → Target y⁺ → Calculate First Layer Height → Generate Inflation Layers → Check Mesh Quality → Run Simulation → Monitor y⁺ → Refine Mesh → Validate Results A major objective of this lecture is to demonstrate that mesh generation is not simply about increasing the number of elements. The mesh must be designed according to the physics, turbulence model, wall treatment, and required y⁺ range. By the end of the lecture, participants will be able to calculate, control, monitor, and interpret y⁺, select suitable first-layer heights and inflation parameters, and develop CFD meshes that provide a balance between accuracy, convergence, and computational cost.