Error-free computation for robust physically-based simulation

Numerical simulation of the physical behaviour for 3D Fluid Dynamics usually requires supercomputing machine computational power to achieve some practical predictive usefulness. Usually, even in that case, minimal boundaries of convergence and stability of computed solutions, or, in other words, the global simulation precision level limits the usefulness of the simulation itself into a narrow operational space-time window. In order to avoid severe degradation of the overall required accuracy for the final global solution in finite computational resource systems, computational error propagation control requires exceptional care. Over the years many correction techniques were developed by either pure computational point of view or numeric representation point of view. In the latter case, the main approaches ranged from factorial-base representation to residue arithmetic and p-adic base number. Unfortunately, they all show practical limitations and do not solve the basic problem for efficient carry/borrow detection minimization. The presented approach operates on a discrete variable domain and solves that problem by offering an arbitrary precision closed solution, based on power series and modular arithmetic. Its implementation on parallel structured multiprocessor architectures is quite straightforward. A numerical example is presented: an optimal computational precision level can be selected according to the required solution accuracy.