Computational engineering / Reproducible scientific computing
Connecting physics, mathematical models, numerical methods, and executable code through carefully verified engineering problems.
Physical reasoning. Explicit assumptions. Inspectable computation.
Free vibration of a mass–spring–damper system
A linear spring, viscous damping, constant coefficients, and no external forcing.
# x: displacement; v: velocity
a = -(c * v + k * x) / m
# Both use the old state
x_next = x + dt * v
v_next = v + dt * adt is Δt (s). Assume m > 0, c ≥ 0, k > 0, and Δt > 0. Every term in the governing equation is a force (N). This code illustrates a discretization; it is not a validated simulation.Method
Identify the system and relevant balance laws. Make units, dimensions, and physical interactions explicit.
State assumptions, variables, parameters, and initial or boundary conditions. Define the model’s domain of validity.
Choose a discretization appropriate to the governing problem. Examine consistency, stability, and convergence.
Translate the method into readable Python, with reproducible inputs and time grids consistent with the update rule.
Compare with analytical or independent reference solutions. Quantify error and distinguish numerical verification from physical validation.
Code execution alone does not establish numerical accuracy. Verification checks the calculation; validation evaluates the model against independent physical evidence.
Investigations
Governing models, executable notebooks,
and the evidence behind the results.
A lumped-capacitance heat-transfer investigation: deriving the cooling model, implementing explicit Euler integration, and checking analytical agreement, step-size convergence, limiting behavior, and discrete energy balance. This is an idealized teaching model, not an experimental measurement.
Areas of study
Fields of interest, rather than a catalogue
of completed work.
About the project
Equation to Code is an independent project devoted to translating governing equations into reproducible computational experiments, with particular attention to physical interpretation, numerical accuracy, and engineering relevance.
The detailed work belongs in version-controlled notebooks and repositories: assumptions, derivations, implementations, experiments, and their limitations.
About the author