The three-dimensional nonlinear evolution of moderate wavelength pressure-driven edge-localized instabilities is calculated in divertor tokamaks. The evolution consists of several stages: linear growth, nonlinear saturation and turbulence, shear flow generation, pressure outflow to the outboard divertor, and finally, outflow to the inboard divertor. The shear flow generation appears to be an important factor in transporting pressure perturbations to the inboard side, and in causing pressure loss to the inboard divertor. The physical model consists of dissipative compressional reduced magnetohydrodynamics which includes the important effect of sound wave propagation. A novel numerical discretization, using a poloidal unstructured mesh and a staggered toroidal mesh, has been implemented on a parallel, distributed memory computer. Nonlinear, three-dimensional numerical computations include a separatrix X-point in the computational domain.