1 Solving Engineering ProblemsFrom physical problem to solution Develop Model Apply Fundamental Principles Obtain Governing Equations Solution of Governing Equations Interpretation of Solution

2 Develop Model Model is developed to represent all important characteristics of the physical system Identify system Identify external influences on system (load, input, output) Material properties (Ideal gas, real gas, Newtonian fluid, Elastic/plastic etc.)

3 Apply Fundamental PrinciplesApply Physical Laws Equilibrium equation Newton's Law of motion Conservation of mass Conservation of momentum Conservation of energy Accounting principle (change = input - output)

4 Obtain governing equationApply simplifying assumptions on the physical laws Derive final governing equation

5 Solution of governing equationSolution may appear as a set of linear/nonlinear algebraic equations Transcendental equations Ordinary differential equations (ODE) Partial differential equations (PDE) Eigenvalue problem The set of simultaneous equations is readily handled using matrices.

6 Solutions of governing equationsTwo types of solutions Closed form mathematical expression leading to analytical solution Closed form not possible, thus needs approximated numerical solution (computers)

7 Solution of governing equation

8 Interpretation of SolutionReality Check Test with simple, known cases Graphics representation better conveys the meaning of solution Graphs Bar charts Contour plots

9 Softwares Languages FORTRAN Matlab C, C++, Python, etc LibrariesNetlib (www.netlib.org) LAPACK EISPACK LINPACK IMSL, etc

10 Softwares Others Octave, Scilab Maxima, Maple Mathematica, MathcadR (statistical) OpenDX, Paraview, Viz5D (plotting, visualization)