ENO-based high-order data-bounded and constrained positivity-preserving interpolation

A number of key scientific computing applications that are based upon tensor-product grid constructions, such as numerical weather prediction (NWP) and combustion simulations, require property-preserving interpolation. Essentially non-oscillatory (ENO) interpolation is a classic example schemes. In the aforementioned application areas, property preservation often manifests itself requirement for either data boundedness or positivity preservation. For example, in NWP, one may have to interpolate between on which dynamics calculated physics (and back). Interpolating density other physical quantities without accounting lead negative values nonphysical result inaccurate representations and/or interpretations data. Property-preserving straightforward when used context low-order simulation methods. High-order is, however, nontrivial, especially case where points not equispaced. this paper, we demonstrate it possible construct high-order methods ensure constrained novel feature algorithm positivity-preserving interpolant constrained; amount by exceeds be strictly controlled. The developed comes with theoretical estimates provide sufficient conditions We our collection 1D 2D examples, show all cases respected.