Research

PUBLICATIONS/PREPRINTS

• J.C. Chrispell, M.W. Farthing, K.R. Fowler, S.E. Howington, E. W. Jenkins, S. Dutta, B. Ji, “Optimization of a managed aquifer recharge network”, Proceedings of the 2014 SC Water Resources Conference, Columbia Metropolitan Convention Center, October 2014. PDF

• P. Daripa, S. Dutta, “Modeling and simulation of surfactant-polymer flooding using a new hybrid method”, Journal of Computational Physics, 335 (2017) 249-282. Link PDF

• S. Dutta, "Mathematical Models and Numerical Methods for Porous Media Flows Arising in Chemical Enhanced Oil Recovery", Ph.D. Dissertation (2017), Texas A&M University. Link

• P. Daripa, S. Dutta, “On the convergence analysis of a hybrid numerical method for multicomponent transport in porous media”, Applied Numerical Mathematics, 146 (2019) 199-220. Link PDF

• S. Dutta, M. W. Farthing, G. Savant, "Model Order Reduction of Parametric and Time-dependent Partial Differential Equations in Computational Fluid Dynamics", To Appear, ERDC Tech Report (2020).

• S. Dutta, M. W. Farthing, E. Perracchione, G. Savant, M. Putti, "A greedy non-intrusive reduced order model for shallow water equations", Journal of Computational Physics, 439 (2021) 110378. Link PDF

• S. Dutta, P. Rivera-Casillas, M. W. Farthing, "Neural ordinary differential equations for data-driven reduced order modeling of environmental hydrodynamics", in Proceedings of the AAAI 2021 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physical Sciences, (2021). PDF

• S. Dutta, P. Rivera-Casillas, O. M. Cecil, M. W. Farthing, E. Perracchione, M. Putti, "Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEs", in Proceedings of the IXth International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2021), (2021). PDF

• S. Dutta, P. Rivera-Casillas, O. M. Cecil, M. W. Farthing, "pyNIROM: A suite of python modules for non-intrusive reduced order modeling of time-dependent problems", Software Impacts, 10 (2021) 100129. Link

• S. Dutta, P. Rivera-Casillas, B. Styles, M. W. Farthing, "Reduced order modeling using advection-aware autoencoders", Mathematical and Computational Applications, 27(3), 34. (2022). Link

SOFTWARE

pyNIROM - An open-source python-based software suite for non-intrusive reduced order modeling. Github Codeocean Capsule

CURRENT RESEARCH

Topic: Reduced Order Modeling in CFD applications

Mentor: Dr. Matthew Farthing

Collaborators: Dr. Emma Perracchione, Dr. Mario Putti, Dr. Gaurav Savant, Mr. Peter Rivera-Casillas, Dr. Orie Cecil

• Computational modeling plays a key role in scientific and engineering analysis both for the US Army Corps of Engineers and the community at large. Many advances in numerical methods for systems of Partial Differential Equations (PDEs) and consistent improvements in processing speed and availability have been made over the past three decades. The reach of high fidelity, physics-based models continues, however, to be limited in many cases by their computational footprint and speed. For this reason, there has been increasing interest in strategies for generating low-dimensional (or reduced) models that are able to run quickly while retaining the accuracy of high-fidelity computations. We consider a family of Model Order Reduction (MOR) techniques based on the idea of projection. In addition to providing an overview of their mathematical formulation for parameterized PDEs, we explore both intrusive strategies for their implementation in legacy software as well as non-intrusive approaches that treat high-fidelity models as a black-box. To evaluate the methods, we consider a range of example problems from linear transport to depth-averaged free surface flow. We focus on the Adaptive Hydraulics (AdH) framework as the high-fidelity model, but the strategies explored are generally applicable to PDE based high-fidelity models under development or supported by the ERDC.

Ph.D. DISSERTATION

Topic: Theory and computation of multicomponent, immiscible, multiphase flow in highly heterogeneous porous media.

Adviser: Dr. Prabir Daripa

• I studied multiphase, multicomponent flows in porous media. These flows arise in a wide range of applications like reservoir simulation, subsurface flows, aquifer remediation processes, biological flows and industrial filtration processes, to name a few. My research has been primarily motivated by studying chemical enhanced oil recovery techniques like polymer flooding and surfactant-polymer (SP) flooding. We proposed a new global pressure function for incompressible, two-phase multicomponent porous media flows. The resulting system of coupled nonlinear partial differential equations were solved using a hybrid numerical methodology. The variable coefficient elliptic pressure equation was solved using a non-traditional Finite Element Method (FEM) that can efficiently handle discontinuities in the coefficient and the solution itself. The transport equations were solved using an implicit time Finite Difference (FD) formulation based on a Modified Method of Characteristics (MMOC) approach.

WORKSHOP

SAMSI Industrial Math/Stat Modeling Workshop

Topic: Pajaro Valley Water Management Mentors : Dr. E. W. Jenkins, Dr. M. W. Farthing

• The project was aimed at designing an optimal network of infiltration basins to replenish depleted underground aquifers using previously uncaptured storm water runoff. We used the realistic test case of a sub-watershed in Pajaro Valley, California. Digital elevation maps and topographical tools were used to delineate subwatershed regions and construct a network along drainage lines. The software CASC-2D was used to compute runoff volumes for a recorded precipitation event in the region. An appropriate cost function was constructed using land and construction costs, local infiltration and subsurface conductivity rates and different optimization algorithms were used to obtain an optimum network. We published our work in the proceedings of the S.C. Water Resources Conference, 2014 in which we concluded that given a target recharge amount tied to the water imbalance in the region, these kinds of feasibility studies and network analyses can help natural resource agencies in water management.

TALKS

• "An optimal RBF-kernel based non-intrusive reduced order model for the shallow water equations", ICIAM 2019 (Valencia, Spain, July 2019)

• "Non-intrusive model reduction via RBF-based kernel methods in varying scale setting", Coupled problems 2019 (Sitges, Spain, June 2019)

• "An Efficient Non-intrusive Reduced Order Model for Approximation of Shallow Water Flows", SIAM Geosciences Meeting 2019 (Houston, March 2019)

• "Reduced Order Modeling for Coastal and Hydraulic Applications in the Corps of Engineers", Industrial and Applied Math Seminar (Texas A&M, November 2018)

• "Effective model reduction for shallow water flows", 7th European Conference on Fluid Dynamics (Glasgow, June 2018)

• "Comparison of intrusive and non-intrusive projection-based model reduction for approximation of free surface flows", Computational Methods in Water Resources XXII (Saint-Malo, June 2018)

• "Dispersive effects on multicomponent transport through porous media", 70th Annual Meeting of the APS Division of Fluid Dynamics (Denver, November 2017)

• “Modeling and simulation of multicomponent, multiphase porous media flows using a new hybrid method”, SIAM Annual Meeting 2017 (Pittsburgh, July 2017)

• “Theory and computation of multiphase, multicomponent flows in porous media”, West Texas Applied Math Graduate Minisymposium (Texas Tech University, Lubbock, TX, April 28, 2017)

• “The mathematics of chemical enhanced oil recovery”, Mathematics Graduate Student Organization Seminar (Texas A&M, April 2017)

• “A modern hybrid method for multiphase, multicomponent flow and transport in porous media”, Texas Differential Equations Conference (College Station, March 4-5, 2017)

• “A numerical study of immiscible two-phase multicomponent flows in highly heterogeneous porous media”, Joint Mathematics Meeting 2017 (Atlanta, January 2017)

• “Modeling and simulation of multicomponent, multiphase porous media flows using a new hybrid method”, Texas A&M Conference on Energy 2016 (Texas A&M, September 2016)

• “Numerical analysis of a hybrid method and large scale simulation results of SP-Flooding”, SIAM Annual Meeting 2016 (Boston, July 2016)

• “Modeling and simulation of multiphase porous media flows using a new hybrid method”, Student Research Week 2016 (Texas A&M, March 2016)

• “Optimization and analysis of a managed aquifer recharge network”, SAMSI Industrial Math/Stat Modeling Workshop 2013 (Raleigh, July 2013)

• “An efficient numerical method for ASP flooding in tertiary oil recovery”, SIAM Geosciences Meeting 2013 (Padova, Italy, June 2013)

• “An efficient numerical method for enhanced oil recovery”, SIAM Annual Meeting 2012 (Minneapolis, July 2012)