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Summary A method of constructing parameterized nonintrusive reduced‐order models (NIROMs) is given. The approach relies on a geometrical interpretation of NIROM, requires only a single layer of interpolation to be applied for both system state and parametric dependence of the model and is applicable to systems characterized by any number of parameters spanning arbitrary orders of magnitude. The method is applied to three representative test problems and evaluated in terms of accuracy and speed, showing good performance.

This work presents a method of exactly and efficiently evaluating integrals of compactly supported (and otherwise) polynomial radial kernels near piecewise-planar boundaries. The technique is motivated by and has an immediate application in the smoothed-particle hydrodynamics method employing the semi-analytical boundary formulation. The current implementation is exact and fully general, avoiding any need for symbolic or numerical integration which previous implementations rely on. A detailed derivation and three compact implementations are provided and the latter can be easily modified to fit new and existing simulation codes. Applications and good performance are demonstrated on a number of test problems, where the semi-analytical boundary method can simulate complex boundaries using roughly half the boundary particles required in a ghost particle boundary method.

We investigate the dynamics, interactions, and decay of immiscible viscous fingers in two and three dimensions over time in a high-aspect ratio (up to 100:1) system. The behavior is related to the viscosity ratio and a macroscopic capillary number. The same four fingering regimes are observed as in miscible displacements (spreading of the interface between wetting and non-wetting fluid but no fingers, the growth of many fingers that can be described by perturbation analysis, non-linear interactions between fingers and decay to a single finger) for low viscosity ratio and high capillary to viscous ratios. At higher viscosity ratios and lower capillary to viscous ratios, periodic tip-splitting and decay results in a fluctuation between one and two fingers at late time. This has not been seen in miscible displacements. We provide a stability plot that can be used to identify when this will occur. Similar behaviors were seen in both two and three dimensions, suggesting that learnings from two-dimensional (2D) linear displacements can be applied to similar three-dimensional (3D) flows. In particular, the square root of the number of fingers seen in the 3D simulations and their decay with time was almost identical to 2D.

A method for modeling mobile spherical solids in Smoothed Particle Hydrodynamics simulations utilizing the semi-analytical boundary formulation is given. The technique relies on evaluating individual contributions from ideally spherical bodies to the normalization factor and its gradient. A derivation is provided in both two and three dimensions (3D) and a close-form solution is given for an arbitrary polynomial kernel function in 3D. The method is validated and implemented in an Smoothed-Particle Hydrodynamics-Discrete Element Method code to evaluate the solid fraction and results are compared to the previous standard.