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Conservation of mass

About: Conservation of mass is a(n) research topic. Over the lifetime, 2387 publication(s) have been published within this topic receiving 57211 citation(s). The topic is also known as: conservation of mass-energy & law of conservation of mass.

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Journal ArticleDOI
Carl Eckart1Institutions (1)
15 Nov 1940-Physical Review
Abstract: The considerations of the first paper of this series are modified so as to be consistent with the special theory of relativity. It is shown that the inertia of energy does not obviate the necessity for assuming the conservation of matter. Matter is to be interpreted as number of molecules, therefore, and not as inertia. Its velocity vector serves to define local proper-time axes, and the energy momentum tensor is resolved into proper-time and -space components. It is shown that the first law of thermodynamics is a scalar equation, and not the fourth component of the energy-momentum principle. Temperature and entropy also prove to be scalars. Simple relativistic generalizations of Fourier's law of heat conduction, and of the laws of viscosity are obtained from the requirements of the second law. The same considerations lead directly to the accepted relativistic form of Ohm's law.

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1,151 citations


Journal ArticleDOI
TL;DR: A new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field that compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution.

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Abstract: In this paper, we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field. Our method uses Lagrangian marker particles to rebuild the level set in regions which are underresolved. This is often the case for flows undergoing stretching and tearing. The overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method. Our method compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The method is presented in three spatial dimensions.

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1,058 citations


Book
01 Jan 1998-
Abstract: Preface List of Symbols CHAPTER 1. DIFFUSIVE FLUXES AND MATERIAL PROPERTIES 1.1 INTRODUCTION 1.2 BASIC CONSTITUTIVE EQUATIONS 1.3 DIFFUSIVITIES FOR ENERGY, SPECIES, AND MOMENTUM 1.4 MAGNITUDES OF TRANSPORT COEFFICIENTS 1.5 MOLECULAR INTERPRETATION OF TRANSPORT COEFFICIENTS 1.6 LIMITATIONS ON LENGTH AND TIME SCALES References Problems CHAPTER 2. FUNDAMENTALS OF HEAT AND MASS TRANSFER 2.1 INTRODUCTION 2.2 GENERAL FORMS OF CONSERVATION EQUATIONS 2.3 CONSERVATION OF MASS 2.4 CONSERVATION OF ENERGY: THERMAL EFFECTS 2.5 HEAT TRANSFER AT INTERFACES 2.6 CONSERVATION OF CHEMICAL SPECIES 2.7 MASS TRANSFER AT INTERFACES 2.8 MOLECULAR VIEW OF SPECIES CONSERVATION References Problems CHAPTER 3. FORMULATION AND APPROXIMATION 3.1 INTRODUCTION 3.2 ONE-DIMENSIONAL EXAMPLES 3.3 ORDER-OF-MAGNITUDE ESTIMATION AND SCALING 3.4 " IN MODELING 3.5 TIME SCALES IN MODELING References Problems CHAPTER 4. SOLUTION METHODS BASED ON SCALING CONCEPTS 4.1 INTRODUCTION 4.2 SIMILARITY METHOD 4.3 REGULAR PERTURBATION ANALYSIS 4.4 SINGULAR PERTURBATION ANALYSIS References Problems CHAPTER 5. SOLUTION METHODS FOR LINEAR PROBLEMS 5.1 INTRODUCTION 5.2 PROPERTIES OF LINEAR BOUNDARY-VALUE PROBLEMS 5.3 FINITE FOURIER TRANSFORM METHOD 5.4 BASIS FUNCTIONS 5.5 FOURIER SERIES 5.6 FFT SOLUTIONS FOR RECTANGULAR GEOMETRIES 5.7 FFT SOLUTIONS FOR CYLINDRICAL GEOMETRIES 5.8 FFT SOLUTIONS FOR SPHERICAL GEOMETRIES 5.9 POINT-SOURCE SOLUTIONS 5.10 MORE ON SELF-ADJOINT EIGENVALUE PROBLEMS AND FFT SOLUTIONS References Problems CHAPTER 6. FUNDAMENTALS OF FLUID MECHANICS 6.1 INTRODUCTION 6.2 CONSERVATION OF MOMENTUM 6.3 TOTAL STRESS, PRESSURE, AND VISCOUS STRESS 6.4 FLUID KINEMATICS 6.5 CONSTITUTIVE EQUATIONS FOR VISCOUS STRESS 6.6 FLUID MECHANICS AT INTERFACES 6.7 FORCE CALCULATIONS 6.8 STREAM FUNCTION 6.9 DIMENSIONLESS GROUPS AND FLOW REGIMES References Problems CHAPTER 7. UNIDIRECTIONAL AND NEARLY UNIDIRECTIONAL FLOW 7.1 INTRODUCTION 7.2 STEADY FLOW WITH A PRESSURE GRADIENT 7.3 STEADY FLOW WITH A MOVING SURFACE 7.4 TIME-DEPENDENT FLOW 7.5 LIMITATIONS OF EXACT SOLUTIONS 7.6 NEARLY UNIDIRECTIONAL FLOW References Problems CHAPTER 8. CREEPING FLOW 8.1 INTRODUCTION 8.2 GENERAL FEATURES OF LOW REYNOLDS NUMBER FLOW 8.3 UNIDIRECTIONAL AND NEARLY UNIDIRECTIONAL SOLUTIONS 8.4 STREAM-FUNCTION SOLUTIONS 8.5 POINT-FORCE SOLUTIONS 8.6 PARTICLES AND SUSPENSIONS 8.7 CORRECTIONS TO STOKES' LAW References Problems CHAPTER 9. LAMINAR FLOW AT HIGH REYNOLDS NUMBER 9.1 INTRODUCTION 9.2 GENERAL FEATURES OF HIGH REYNOLDS NUMBER FLOW 9.3 IRROTATIONAL FLOW 9.4 BOUNDARY LAYERS AT SOLID SURFACES 9.5 INTERNAL BOUNDARY LAYERS References Problems CHAPTER 10. FORCED-CONVECTION HEAT AND MASS TRANSFER IN CONFINED LAMINAR FLOWS 10.1 INTRODUCTION 10.2 PECLET NUMBER 10.3 NUSSELT AND SHERWOOD NUMBERS 10.4 ENTRANCE REGION 10.5 FULLY DEVELOPED REGION 10.6 CONSERVATION OF ENERGY: MECHANICAL EFFECTS 10.7 TAYLOR DISPERSION References Problems CHAPTER 11. FORCED-CONVECTION HEAT AND MASS TRANSFER IN UNCONFINED LAMINAR FLOWS 11.1 INTRODUCTION 11.2 HEAT AND MASS TRANSFER IN CREEPING FLOW 11.3 HEAT AND MASS TRANSFER IN LAMINAR BOUNDARY LAYERS 11.4 SCALING LAWS FOR NUSSELT AND SHERWOOD NUMBERS References Problems CHAPTER 12. TRANSPORT IN BUOYANCY-DRIVEN FLOW 12.1 INTRODUCTION 12.2 BUOYANCY AND THE BOUSSINESQ APPROXIMATION 12.3 CONFINED FLOWS 12.4 DIMENSIONAL ANALYSIS AND BOUNDARY-LAYER EQUATIONS 12.5 UNCONFINED FLOWS References Problems CHAPTER 13. TRANSPORT IN TURBULENT FLOW 13.1 INTRODUCTION 13.2 BASIC FEATURES OF TURBULENCE 13.3 TIME-SMOOTHED EQUATIONS 13.4 EDDY DIFFUSIVITY MODELS 13.5 OTHER APPROACHES FOR TURBULENT-FLOW CALCULATIONS References Problems CHAPTER 14. SIMULTANEOUS ENERGY AND MASS TRANSFER AND MULTICOMPONENT SYSTEMS 14.1 INTRODUCTION 14.2 CONSERVATION OF ENERGY: MULTICOMPONENT SYSTEMS 14.3 SIMULTANEOUS HEAT AND MASS TRANSFER 14.4 INTRODUCTION TO COUPLED FLUXES 14.5 STEFAN-MAXWELL EQUATIONS 14.6 GENERALIZED DIFFUSION IN DILUTE MIXTURES 14.7 GENERALIZED STEFAN-MAXWELL EQUATIONS References Problems CHAPTER 15. TRANSPORT IN ELECTROLYTE SOLUTIONS 15.1 INTRODUCTION 15.2 FORMULATION OF MACROSCOPIC PROBLEMS 15.3 MACROSCOPIC EXAMPLES 15.4 EQUILIBRIUM DOUBLE LAYERS 15.5 ELECTROKINETIC PHENOMENA References Problems APPENDIX A. VECTORS AND TENSORS A.1 INTRODUCTION A.2 REPRESENTATION OF VECTORS AND TENSORS A.3 VECTOR AND TENSOR PRODUCTS A.4 VECTOR-DIFFERENTIAL OPERATORS A.5 INTEGRAL TRANSFORMATIONS A.6 POSITION VECTORS A.7 ORTHOGONAL CURVILINEAR COORDINATES A.8 SURFACE GEOMETRY References APPENDIX B. ORDINARY DIFFERENTIAL EQUATIONS AND SPECIAL FUNCTIONS B.1 INTRODUCTION B.2 FIRST-ORDER EQUATIONS B.3 EQUATIONS WITH CONSTANT COEFFICIENTS B.4 BESSEL AND SPHERICAL BESSEL EQUATIONS B.5 OTHER EQUATIONS WITH VARIABLE COEFFICIENTS References Index

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1,056 citations


Journal ArticleDOI
Elin Olsson1, Gunilla Kreiss2, Sara Zahedi1Institutions (2)
Abstract: In this paper, we continue to develop and study the conservative level set method for incompressible two phase flow with surface tension introduced in [J. Comput. Phys. 210 (2005) 225-246]. We formulate a modification of the reinitialization and present a theoretical study of what kind of conservation we can expect of the method. A finite element discretization is presented as well as an adaptive mesh control procedure. Numerical experiments relevant for problems in petroleum engineering and material science are presented. For these problems the surface tension is strong and conservation of mass is important. Problems in both two and three dimensions with uniform as well as non-uniform grids are studied. From these calculations convergence and conservation is studied. Good conservation and convergence are observed.

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956 citations


Book
01 Jan 1940-
Abstract: The existing analytical treatments of ground-water flow have mostly been founded upon the erroneous conception, borrowed from the theory of the flow of the ideal frictionless fluids of classical hydrodynamics, that ground-water motion is derivable from a velocity potential. This conception is in conformity with the principle of the conservation of matter but not with that of the conservation of energy. In the present paper it is shown that a more exceptionless analytical theory results if a potential whose value at a given point is defined to be equal to the work required to transform a unit mass of fluid from an arbitrary standard state to the state at the point in question is employed. Denoting this function by $$\Phi$$, it is shown that the differential equation of fluid flow in an isotropic medium is given by $$q = - \sigma$$ grad $$\Phi$$, where q is the flow vector whose magnitude is equal to the volume of fluid crossing a unit of area normal to the flow direction in unit time, and $$\sigma$$ a spec...

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700 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20229
2021115
2020112
2019105
201899
201793

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Topic's top 5 most impactful authors

Brahim Amaziane

5 papers, 29 citations

Zhenquan Li

4 papers, 25 citations

Shuyu Sun

4 papers, 53 citations

Klemens Fellner

4 papers, 55 citations

Sharif Abdullah Al-Mamun

3 papers, 21 citations