An Artificial Compressibility Ensemble Timestepping Algorithm for Flow Problems
For researchers in computational fluid dynamics, this algorithm enables larger ensemble sizes for uncertainty quantification by reducing computational costs.
The paper introduces a first-order artificial compressibility ensemble algorithm that decouples velocity and pressure solves to reduce computational complexity and storage for ensemble calculations in flow problems with uncertain data. Numerical tests confirm theoretical stability and convergence.
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.