MECN4039A Tools III — Lectures 1 & 2: Study Notes, Flashcards, and Practice Test Flashcards

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Project-based course

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A course format where learning revolves around completing practical projects that integrate theory and computational tools, often linked to real engineering streams and specialist modules.

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Assessment components

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The course assessment is split across written tests, tutorial/super-tutorials, two major assignments (FEA/CFD/DES), and exam-equivalent model assessments, each carrying specific percentage weights.

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Single precision

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A floating-point format using 32 bits of storage that provides about 7 decimal digits of precision and is faster but less accurate than double precision.

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Double precision

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A floating-point format using 64 bits that offers roughly 16 decimal digits of precision, reducing rounding errors at the cost of more memory and computation.

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Truncation error

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Error that arises when an infinite process (like a series) is approximated by a finite number of terms; it accumulates when numerical approximations truncate exact expressions.

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Rounding error

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Error caused when real numbers are rounded to the nearest representable floating-point value, which can accumulate across many operations.

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PRNG

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A pseudo-random number generator produces deterministic sequences based on a seed using formulas such as the linear congruential generator, useful for stochastic simulations but inherently periodic.

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Box–Muller

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A transform that converts two independent uniform random variables into two independent standard normal variables using $Z_0 = \sqrt{-2\ln U_1}\cos(2\pi U_2)$ and $Z_1 = \sqrt{-2\ln U_1}\sin(2\pi U_2)$.

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Quadrature

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Numerical integration methods (e.g., trapezoidal, Simpson, Gaussian) used to approximate integrals of functions when analytic integration is infeasible.

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Finite differences

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Discrete approximations to derivatives using nearby function values (forward, backward, central schemes) often used to discretise differential operators.

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Dirichlet BC

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A boundary condition that prescribes the exact value of the solution variable at the boundary (e.g., fixed temperature or fixed displacement).

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Neumann BC

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A boundary condition that prescribes the derivative or flux of the solution normal to the boundary, often representing heat flux or stress.

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Discretisation

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The process of breaking continuous mathematical domains (space/time) into discrete parts so they can be approximated numerically, such as meshes or time steps.

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Resolution

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The smallest scale or level of detail that the discretised model can represent; higher resolution captures finer features but increases computational cost.

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Biased discretisation

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A discretisation strategy that concentrates higher resolution in regions with large gradients or significant features to improve accuracy without uniformly increasing cost.

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Residual

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The difference between the left- and right-hand side of the discretised governing equations (a measure of mathematical consistency), not necessarily equal to the physical error.

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Verification

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The process of ensuring the computational model was implemented correctly, typically via comparison with analytical solutions, alternative solvers, or known benchmarks.

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Validation

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Checking that the model accurately represents reality by comparing simulation results to experimental or published physical data; verification and validation together build confidence.

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Workflow steps

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A general modelling workflow includes identifying the phenomenon, selecting methods, defining the domain, choosing solvers and BCs, solving, monitoring convergence, verifying/validating, and post-processing.