Johnny Corbino is an HPC Applications Engineer in the Computer Languages and Systems Software Group. Before joining CLaSS, Johnny worked in The Netherlands for ASML as Software Engineer. His research interests combine high-performance computing, mathematical modeling, and artificial intelligence. He earned his Ph.D. in Computational Science from Claremont Graduate University in 2018.
J Corbino, J Castillo, "High-order mimetic finite-difference operators satisfying the extended Gauss divergence theorem", Journal of Computational and Applied Mathematics, 2020, doi: 10.1016/j.cam.2019.06.042
We present high-order mimetic finite-difference operators that satisfy the extended Gauss theorem. These operators have the same order of accuracy in the interior and at the boundary, no free parameters and optimal bandwidth. They are defined over staggered grids, using weighted inner products with a diagonal norm. We present several examples to demonstrate that mimetic finite-difference schemes using these operators produce excellent results.
A Boada, J Corbino, J Castillo, "High-order mimetic difference simulation of unsaturated flow using Richards equation", Mathematics in Applied Sciences and Engineering, 2020, doi: 10.5206/mase/10874
The vadose zone is the portion of the subsurface above the water table and its pore space usually contains air and water. Due to the presence of infiltration, erosion, plant growth, microbiota, contaminant transport, aquifer recharge, and discharge to surface water, it is crucial to predict the transport rate of water and other substances within this zone. However, ow in the vadose zone has many complications as the parameters that control it are extremely sensitive to the saturation of the media, leading to a nonlinear problem. This ow is referred as unsaturated ow and is governed by Richards equation. Analytical solutions for this equation exists only for simplified cases, so most practical situations require a numerical solution. Nevertheless, the nonlinear nature of Richards equation introduces challenges that causes numerical solutions for this problem to be computationally expensive and, in some cases, unreliable. High-order mimetic finite difference operators are discrete analogs of the continuous differential operators and have been extensively used in the fields of fluid and solid mechanics. In this work, we present a numerical approach involving high-order mimetic operators along with a Newton root- finding algorithm for the treatment of the nonlinear component. Fully-implicit time discretization scheme is used to deal with the problem's stiffness.
J Corbino, J Castillo, C Paolini, "SubFlow: An open-source, object-oriented application for modeling geologic storage of CO2", Journal of Hydrologic Engineering, 2016, doi: 10.1190/ice2016-6517529.1
The capture of carbon dioxide for its subsequent storage in brine-saturated reservoirs or depleted oil fields has become a significant part of US energy policy. In this work, we focus on the design and development of a novel CCUS application to model carbon dioxide injection in brine-saturated reservoirs. SubFlow is written in C++ and uses a relational database to store user session and simulation parameters such as mineral, solute, kinetic reaction, lithology, formation, and injection water data. Subflow is capable of 3D real-time visualization, distributed-parallel execution on massively parallel processor (MPP) systems using OpenMP and MPI, and features an intuitive user interface developed using Qt. SubFlow uses a mimetic discretization method (MDM) for solving conservation of solute mass, energy, and fluid momentum, and the finite element method for solving the pressure, rock stress, and fracture fields. SubFlow is implemented with the Mimetic Methods Toolkit (MTK), a C++ API which allows for an intuitive implementation of the Castillo-Grone based Mimetic Discretization Methods. The FVM is second order accurate while the MDM is capable of fourth order accuracy. OpenGL is used to render pressure, temperature, stress, velocity, and solute concentration fields on a 3D mesh that represents a reservoir. Results from selected simulations are compared with those produced by TOUGHREACT and STOMP.