Governing Equations I: reference equations at the scale of the continuum

Jun 12, 2013

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Overview. Introduction : from molecules to

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Governing Equations I: reference equations at the scale of the continuum

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Governing Equations II: classical approximations and other systems of equations

Governing Equations II: classical approximations and other systems of equations. By Sylvie Malardel (room 10a; ext. 2414) after Nils Wedi (room 007; ext. 2657). Thanks to Clive Temperton, Mike Cullen and Piotr Smolarkiewicz. The continuous set of dry adiabatic equations.

953 views • 37 slides

Governing Equations V

Governing Equations V. by Nils Wedi (room 007; ext. 2657). Thanks to Piotr Smolarkiewicz and Peter Bechtold. Introduction and motivation. How do we treat artificial and/or natural boundaries and how do these influence the solution ?

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Governing Equations IV

Introduction. Nonhydrostatic model NH - IFSPhysics - Dynamics coupling. Introduction A history. Resolution increases of the deterministic 10-day medium-range Integrated Forecast System (IFS) over ~25 years at ECMWF:1987: T 106 (~125km)1991: T 213 (~63km)1998: TL319 (~63km)2000: TL511 (~39km)

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Governing Equations II

Governing Equations II. by Nils Wedi (room 007; ext. 2657). Thanks to Piotr Smolarkiewicz. Introduction. Continue to review and compare a few distinct modelling approaches for atmospheric and oceanic flows

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Governing Equations IV

Governing Equations IV. by Nils Wedi (room 007; ext. 2657). Thanks to Piotr Smolarkiewicz , Glen Shutts and Peter Bechtold. Introduction and motivation. How do we treat artificial and/or natural boundaries and how do these influence the solution ?

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The Equations of Tribocharging

The Equations of Tribocharging. Brian Young 26 January 2009 Reference: “ The Static Electrification of Particles in Gas-Solids Pipe Flow” – Komatsu, 1976 . Fundamental Equation. Equation defines the average charge/mass ratio Essentially linear when n(x ) is much smaller than n0

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Governing Equations III

Governing Equations III. by Nils Wedi (room 007; ext. 2657). Thanks to Anton Beljaars. Introduction. Mass-based hydrostatic and nonhydrostatic models The IFS equations Physics - Dynamics coupling. Introduction.

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The Arithmetic of Equations. Section 9.1. Interpreting Chemical Equations. In terms of moles : Example Equation: 2H 2 + O 2  2H 2 O. 2 mol H2 +. 1 mol O2 = . 2 mol H2O . Interpreting Chemical Equations. In terms of particles:

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The equations of motion. The equations of motion can be used when an object is accelerating at a steady rate There are four equations relating five quantities u initial velocity, v final velocity, s displacement, a acceleration, t time SUVAT equations. Beware!.

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The Math of Equations. Stoichiometry the calculation of quantities in chemical reactions. Limiting Reactant. Calculate the amount of product that could be made for each reactant

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The Governing Equations

time step update. Finite difference form of x momentum equation is arranged to the following form: Coefficients of {F1X k , F2X k , GX k } are obtained form calculation. Finite difference form of y momentum equation is arranged to the following form:

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-1. Full Cell VOF 1. Partial Cell VOF . Empty Cell VOF 0. 2. 1. 0. Penn State Computation Day. Staggered Mesh. Computational Setup. Tube Wall ( r = R ). radial velocity, u. (i, j+1). (i+1, j+1). Computational grid for axisymmetric motion of a drop in a cylindrical tube.

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The Equations of Motion. Euler angle rate equations:. Sensors. Acceleration Measurement ADXL105EM-3 (Triple axis accelerometer) Range = ± 4g Sensitivity ~ 500mv/g Operating Voltage = 5 V DC. Rate Measurement Microgyro 100 (Dual axis rate gyroscope) Range = ± 100°/sec

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Governing Equations I

Governing Equations I. by Clive Temperton (room 124) and Nils Wedi (room 128). Overview. Introduction Fundamental physical principles Eulerian vs. Lagrangian derivatives Continuity equation Thermodynamic equation Momentum equation (in rotating reference frame) Spherical coordinates.

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Governing Equations II. by Clive Temperton (room 124) and Nils Wedi (room 128). Overview. Scale analysis of momentum equations Geostrophic and hydrostatic relations Eta – vertical coordinate Putting it all together -- ECMWF’s equations Map projections and alternative spherical coordinates

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The Equations of State. (YAC: 2-7 through 2-10; 3-6 through 3-7). Equations that relate the pressure, temperature, and specific volume of a substance. They predict the p-v-T relationship of a “ gas ” reasonably well within selected regions. The most well-known is the: Ideal gas equation:.

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Governing Equations in Differential Form. Take the limit such that the control volume approach to infinitesimal small: consequently, all fluid properties within the volume can be considered constant.

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Basic Governing Differential Equations. CEE 331 November 18, 2014. Overview. Continuity Equation Navier-Stokes Equation (a bit of vector notation...) Examples (all laminar flow) Flow between stationary parallel horizontal plates Flow between inclined parallel plates

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Basic Governing Differential Equations

Basic Governing Differential Equations. CEE 331 January 4, 2020. Overview. Continuity Equation Navier-Stokes Equation (a bit of vector notation...) Examples (all laminar flow) Flow between stationary parallel horizontal plates Flow between inclined parallel plates

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