High-Performance Aerospace Computing with Fortran

The fast numerical core under aerospace: write the solver kernels in Fortran, the language of CFD, FEA, and HPC.

10 projects, 250 hands-on levels, run in your browser.

Syllabus

  • Fortran for Numerics: Foundations: Fortran (Formula Translation) has been the language of high-performance scientific computing since 1957, and it still runs the aerospace world's CFD solvers, structural codes, and HPC kernels. Start at the foundations: precise numeric types, procedures, control flow, and the building blocks you will assemble into real solvers. Your code is compiled with gfortran on the server, the same toolchain used on real clusters.
  • Arrays: Fortran's Superpower: Arrays are why Fortran dominates numerical computing. Go beyond single vectors into multidimensional arrays, slicing, and the array intrinsics that express whole computations in one line: matmul, transpose, sum over a dimension, and masked operations. This is the level of expressiveness and speed that makes Fortran the language of CFD, FEA, and HPC kernels.
  • Procedures and Modules: Real numerical software is organized into reusable modules of well-designed procedures, the way NASTRAN and modern CFD codes are built. Master pure and elemental procedures, flexible interfaces with optional and keyword arguments, passing procedures as arguments (the key to generic numerical methods), recursion, generic interfaces, and assembling it all into a clean library.
  • Numerical Methods: The classic algorithms of computational engineering, built on the procedure-argument machinery from Project 3. Find roots of equations by bisection and Newton's method, interpolate data tables, and integrate functions with the trapezoid and Simpson rules. These are the methods that solve the equations physics hands you when there is no formula for the answer.
  • Differential Equations and Dynamics: Most of physics is differential equations: rules for how things change over time. Integrating them numerically is how you simulate motion. Build Euler's method and the workhorse Runge-Kutta (RK4), extend them to systems of equations, and simulate real dynamics, a harmonic oscillator, a projectile with drag, and a two-body orbit that conserves energy.
  • Linear Algebra: The Solver Core: Almost every engineering simulation comes down to solving a linear system A x = b: structures, circuits, fluid grids, all produce one. Build the solver from scratch: back substitution, Gaussian elimination with pivoting, LU decomposition, the fast tridiagonal (Thomas) algorithm, and iterative Jacobi. This is the computational core of BLAS and LAPACK.
  • Finite Differences and CFD Kernels: Computational fluid dynamics and heat transfer discretize space into a grid and approximate derivatives by finite differences. Build the difference operators, solve the 1D heat equation (with its stability limit), transport a pulse by advection, and relax a 2D temperature field to steady state, the kernels at the heart of CFD codes like the ones NASA runs.
  • The Finite Element Method: The finite element method is how aerospace analyzes structures, it is the math inside NASTRAN. Build it from scratch for axial (spring and bar) elements: the element stiffness matrix, assembling elements into a global system, applying supports and loads, solving for displacements, and recovering stresses. The structural-analysis core, from first principles.
  • Performance and Parallelism: Why Fortran is the language of high-performance computing. Write code that respects the machine: column-major memory order for cache efficiency, whole-array operations the compiler vectorizes, do concurrent loops ready for parallel execution, efficient reductions and scans, and a tuned numerical kernel. The difference between code that runs and code that flies.
  • Capstone: A Sounding Rocket: The grand finale: simulate and analyze a sounding rocket, bringing together everything in the track. Model its forces and equations of motion, integrate the ascent with RK4, compute mission performance (max velocity, impulse, apogee, peak dynamic pressure), check the structure against its loads, and assemble a complete mission report. From Fortran fundamentals to a full aerospace simulation.

Key concepts

  • Computational fluid dynamics (CFD): Simulating fluid flow by discretizing the governing equations on a grid and stepping them forward, a core HPC workload.
  • Convergence: An iterative method converges when successive approximations stop changing within a tolerance, the signal to stop iterating.
  • Double precision: 64-bit floating-point (real64), the workhorse type for scientific numerics where rounding error must stay small.
  • Finite element method (FEM): Solving structural and field problems by breaking a domain into small elements and assembling a global stiffness matrix into a linear system.
  • Finite-difference method: Approximating derivatives by differences of nearby grid values, the basis of numerically solving differential equations on a grid.
  • Gaussian elimination: The standard direct method to solve Ax = b by row-reducing A to triangular form, then back-substituting.
  • Linear system (Ax = b): A set of linear equations solved for the unknown vector x; ubiquitous in engineering (structures, circuits, discretized PDEs).
  • Module: A Fortran container for reusable procedures, types, and constants, the unit of code organization in modern HPC Fortran.
  • ODE integration: Marching a differential equation forward in time in small steps (Euler, Runge-Kutta), the engine of simulation.
  • Stencil: A fixed pattern of neighboring grid points used to update each cell (e.g., a 3-point Laplacian), the inner loop of grid-based solvers.
  • Stiffness matrix: In FEM, the matrix K relating displacements to forces (K u = f); assembled from element contributions.