Nonmodal instability of PDE discretizations  – Secondary Instability and Floquet Analysis

Velocity components of the Floquet mode. Introduction The main principle of secondary instability could be described as follows: when disturbances add up to a basic undisturbed flow, they grow such that their amplitude could be described as finite. As a result from the main instability they may achieve saturation characterized in a way as a …

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Nonmodal instability of PDE discretizations – Transient growth through the mathematical standpoint – An introduction primer to bypass transition

Beginnings The basis of the explanation is based on Ellingsen and Palm (1974), although i have made some alterations for practical reasons.Rayleigh showed at 1880 that the necessary condition for instability of a non-viscous flow is an Inflection point in the velocity profile. This criterion was sharpened by Fjortof that showed that in addition there …

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From Reynolds Transport Theorem to Navier-Cauchy to Navier-Stokes Voyage: Part II

In part I of this blog, we have discussed the evolvement of the Conservation of Linear Momentum Equation from Newton's Second Law of Motion using Reynolds Transport Theorem. During the process we covered what is the need of Reynolds Transport Theorem, The Forcing & Stress Tensor Concept in Fluid: Fluid Kinematics Perspective, derived Cauchy Theorem, …

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From Reynolds Transport Theorem to Navier-Cauchy to Navier-Stokes Voyage: Part I

There are certain fundamental principles of conservation that govern the implementation of CFD. These principles are Conservation of mass, momentum & energy. We will see how we can represent these principles evolve in a mathematical form that expresses the dynamics of fluid flow by preserving mass, momentum and energy conservation. The Need of Reynolds Transport …

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SIMPLE Algorithm: Way to solve incompressible NV-Stokes Equation

Introduction Transport equations for each velocity component – momentum equations – can be derived from the general transport equation by replacing the variable φ with u, v and w respectively. The above equations govern a two-dimensional laminar steady flow. The Main Problem! The velocity field obtained from the momentum equation must also satisfy the continuity …

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