Conservation of mass

In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass cannot change, so the quantity can neither be added nor be removed. Therefore, the quantity of mass is conserved over time. The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form. For example, in chemical reactions, the mass of the chemical components before the reaction is equal to the mass of the components after the reaction. Thus, during any chemical reaction and low-energy thermodynamic processes in an isolated system, the total mass of the reactants, or starting materials, must be equal to the mass of the products. The concept of mass conservation is widely used in many fields such as chemistry, mechanics, and fluid dynamics. Historic

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Controlling oscillations in spectral schemes using Artificial Neural Networks

Lukas Schwander

Global Fourier spectral methods are excellent tools to solve conserva- tion laws. They enable fast convergence rates and highly accurate solutions. However, being high-order methods, they suffer from the Gibbs phenomenon, which leads to spurious numerical oscillations in the vicinity of discontinuities. This can have a detrimental effect on the solution quality and lead to unphysical results. While local approxima- tion techniques allow for local limiting or reconstruction, there are no such possibilities for global methods. This thesis proposes a neural net- work based method that adds artificial viscosity around discontinuities of the solution to the conservation law. This enables the transforma- tion of discontinuities into steep but continuous jumps. Test cases in one and two spatial dimensions as well as systems of conservation laws (Euler equations) are solved. Furthermore, the method is generalized to other global basis approaches on non-uniform grids and reduced ba- sis methods. The proposed method delivers satisfactory results in all test cases. On the one hand, it is able to detect and handle discontinu- ities. On the other hand, it stays highly accurate for smooth data.

2020

Regularity of solutions for a fourth-order elliptic system via Conservation law

Changyu Guo

In this paper, we obtain interior Holder continuity for solutions of the fourth-order elliptic system Delta(2)u = Delta(V center dot del u) + div(w del u) + W center dot del u formulated by Lamm and Riviere [Comm. Partial Differential Equations 33 (2008) 245-262]. Boundary continuity is also obtained under a standard Dirichlet or Navier boundary condition. We also use conservation law to establish a weak compactness result which generalizes a result of Riviere for the second-order problem.

2019

Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks

Jan Sickmann Hesthaven, Deep Ray, Lukas Schwander

While a nonlinear viscosity is used widely to control oscillations when solving conservation laws using high-order elements based methods, such techniques are less straightforward to apply in global spectral methods since a local estimate of the solution regularity is generally required. In this work we demonstrate how to train and use a local artificial neural network to estimate the local solution regularity and demonstrate the efficiency of nonlinear artificial viscosity methods based on this, in the context of Fourier spectral methods. We compare with entropy viscosity techniques and illustrate the promise of the neural network based estimators when solving one- and two-dimensional conservation laws, including the Euler equations. (C) 2021 Elsevier Inc. All rights reserved.

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

MATH-459: Numerical methods for conservation laws

Introduction to the development, analysis, and application of computational methods for solving conservation laws with an emphasis on finite volume, limiter based schemes, high-order essentially non-oscillatory schemes, and discontinuous Galerkin methods.

ME-451: Advanced energetics

Methods for the rational use and conversion of energy in industrial processes : how to analyse the energy usage, calculate the heat recovery by pinch analysis, define heat exchanger network, integrate heat pumps and cogeneration units and realise exergy analysis of energy conversion systems.

ME-251: Thermodynamics and energetics I

Introduction aux principes de la thermodynamique, propriétés thermodynamiques de la matière et à leur calcul. Les étudiants maîtriseront les concepts de conservation (chaleur, masse, quantité de mouvement) et appliqueront ces concepts au cycles thermodynamiques et systèmes de conversion d'énergie.

Chemistry

Chemistry is the scientific study of the properties and behavior of matter. It is a physical science under natural sciences that covers the elements that make up matter to the compounds made of atoms,

Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. Phy

Conservation of energy

In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. Energy can neither be created no