Numerical simulation of compressible flow using a velocity/vorticity/pressure formulation

The fundamental equations for compressible flow are solved using a velocity - pressure - vorticity formulation producing a solution that satisfies continuity and vorticity definitions up to machine accuracy. Chapter 1 reviews many algorithms used to solve this problem. Unlike those methods, no pressure - velocity relation or artificial compressibility is assumed in the present formulation, so the equations for kinematics, pressure and momentum are decoupled independent building blocks in the iterative process. As a consequence, the resulting modular algorithm can be used directly for compressible or incompressible flows, contrasting with other current techniques. Moreover the present formulation also applies to two-dimensional and three-dimensional, structured and unstructured grids without any changes, even though only the two-dimensional version was implemented. In Chapter 2, the original formulation is described. A functional minimization technique is used to discretize the kinematics equations, mimicking continuous methods used in the field of functional analysis and providing a common framework to understand, model and implement the solution algorithm. Suitable preconditioning and radial interpolation techniques are employed to balance precision and computational speed. The Poisson equation for pressure is solved similarly by minimizing a suitable functional. The momentum equations are then solved using a finite volume approach adding a controlled amount of artificial viscosity according to mesh size and Reynolds number, resulting in a stable calculation. The vorticity is then obtained as the curl of the velocity. Temperature is similarly computed from the energy equation in an outer loop. Suitable adjustments to pressure and temperature enable the ideal gas equation to fit both the compressible and incompressible paradigms Subsequent chapters deal with validation, applying the computer efficient implementation of the algorithm to a variety of well documented aerodynamic benchmark problems. Examples include compressible and incompressible flow, steady and unsteady problems and flow over cylinders and airfoils over a variety of Reynolds and subsonic Mach numbers.