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