  Ensemble calculations are essential for systems with uncertain data but
require substantial increase in computational resources. This increase severely
limits ensemble size. To reach beyond current limits, we present a first-order
artificial compressibility ensemble algorithm. This algorithm effectively
decouples the velocity and pressure solve via artificial compression, thereby
reducing computational complexity and execution time. Further reductions in
storage and computation time are achieved via a splitting of the convective
term. Nonlinear energy stability and first-order convergence of the method are
proven under a CFL-type condition involving fluctuations of the velocity.
Numerical tests are provided which confirm the theoretical analyses and
illustrate the value of ensemble calculations.
