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lecture 1

# lecture 1 - CE 30125 Lecture 1 LECTURE 1 INTRODUCTION...

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CE 30125 - Lecture 1 p. 1.1 LECTURE 1 INTRODUCTION Formulating a “Mathematical” Model versus a Physical Model Formulate the fundamental conservation laws to mathematically describe what is physi- cally occurring. Also define the necessary constitutive relationships (relate variables based on observations) and boundary conditions (b.c.’s) and/or compatibility constraints. Use the laws of physics applied to an object/domain to develop the governing equations. Algebraic equations Integral equations valid for the domain as a whole p.d.e.’s valid at every point within the domain • e.g. Newton’s 2nd law applied to a point in a hypothetical continuum Navier- Stokes equations Solve the resulting equations using • Analytical solutions • Numerical or discrete solutions Verify how well you have solved the problem by comparing to measurements

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CE 30125 - Lecture 1 p. 1.2 INSERT FIGURE NO. 115 Physical System Numerical Solution Governing Equations Nature Numbers Set of Mathematical Equations ERROR 1: Formulation Error ERROR 3: Data Errors ERROR 2: Numerical Errors Engineering modelers should distinguish Formulation Errors, Numerical Discretization Errors and Data Errors A MATHEMATICAL MODEL