Numerical method for Darcy flow derived using Discrete Exterior Calculus. - Anil N. Hirani; K. B. Nakshatrala; Jehanzeb Hameed Chaudhry (CoRR, 2008)

On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problem - Daniel Z. Turner; K. B. Nakshatrala; K. D. Hjelmstad (CoRR, 2008)

Consistent Newton-Raphson vs. fixed-point for variational multiscale formulations for incompressible Navier-Stokes - Daniel Z. Turner; K. B. Nakshatrala; K. D. Hjelmstad (CoRR, 2008)

A stabilized finite element formulation for advection-diffusion using the generalized finite element framework - Daniel Z. Turner; K. B. Nakshatrala; K. D. Hjelmstad (CoRR, 2008)

Variational structure of the optimal artificial diffusion method for the advection-diffusion equation - K. B. Nakshatrala; Albert J. Valocchi (CoRR, 2009)

A numerical study of fluids with pressure dependent viscosity flowing through a rigid porous media - K. B. Nakshatrala; K. R. Rajagopal (CoRR, 2009)

On dual Schur domain decomposition method for linear first-order transient problems. - K. B. Nakshatrala; Arun Prakash; K. D. Hjelmstad (J. Comput. Phys., 2009)

Non-negative mixed finite element formulations for a tensorial diffusion equation. - K. B. Nakshatrala; Albert J. Valocchi (J. Comput. Phys., 2009)

Enforcing non-negativity constraint and maximum principles for diffusion with decay on general computational grids - Harsha Nagarajan; K. B. Nakshatrala (CoRR, 2010)

A stabilized mixed formulation for unsteady Brinkman equation based on the method of horizontal lines - S. Srinivasan; K. B. Nakshatrala (CoRR, 2010)

On the performance of the variational multiscale formulation for subsurface flow and transport in heterogeneous porous media - Daniel Z. Turner; K. B. Nakshatrala; P. K. Notz (CoRR, 2010)

On the vibrations of lumped parameter systems governed by differential-algebraic equations. - Swaroop Darbha; K. B. Nakshatrala; K. R. Rajagopal (J. Frankl. Inst., 2010)

A mixed formulation for a modification to Darcy equation based on Picard linearization and numerical solutions to large-scale realistic problems. - K. B. Nakshatrala; Daniel Z. Turner (CoRR, 2011)

A framework for coupled deformation-diffusion analysis with application to degradation/healing - Maruti Kumar Mudunuru; K. B. Nakshatrala (CoRR, 2011)

On the performance of high-order finite elements with respect to maximum principles and the non-negative constraint for diffusion-type equations. - G. S. Payette; K. B. Nakshatrala; J. N. Reddy 001 (CoRR, 2011)

A numerical methodology for enforcing maximum principles and the non-negative constraint for transient diffusion equations - K. B. Nakshatrala; Harsha Nagarajan (CoRR, 2012)

Modification to Darcy model for high pressure and high velocity applications and associated mixed finite element formulations. - Justin Chang 001; K. B. Nakshatrala (CoRR, 2013)

A framework for coupling flow and deformation of the porous solid - Daniel Z. Turner; K. B. Nakshatrala; M. J. Martinez (CoRR, 2013)

A numerical framework for diffusion-controlled bimolecular-reactive systems to enforce maximum principles and the non-negative constraint. - K. B. Nakshatrala; Maruti Kumar Mudunuru; Albert J. Valocchi (J. Comput. Phys., 2013)

A monolithic multi-time-step computational framework for advective-diffusive-reactive transient systems with disparate scales. - S. Karimi; K. B. Nakshatrala (CoRR, 2014)

On multi-time-step monolithic coupling algorithms for elastodynamics. - S. Karimi; K. B. Nakshatrala (J. Comput. Phys., 2014)

Do current lattice Boltzmann methods for diffusion-type equations respect maximum principles and the non-negative constraint? - S. Karimi; K. B. Nakshatrala (CoRR, 2015)

On mesh restrictions to satisfy comparison principles, maximum principles, and the non-negative constraint: Recent developments and new results. - Maruti Kumar Mudunuru; K. B. Nakshatrala (CoRR, 2015)

On mechanics-based a posteriori criteria to assess accuracy of numerical solutions for Darcy and Darcy-Brinkman equations. - M. Shabouei; K. B. Nakshatrala (CoRR, 2015)

Material degradation due to moisture and temperature. Part 1: Mathematical model, analysis, and analytical solutions. - C. Xu; Maruti Kumar Mudunuru; K. B. Nakshatrala (CoRR, 2015)

Variational inequality approach to enforce the non-negative constraint for advection-diffusion equations. - Justin Chang 001; K. B. Nakshatrala (CoRR, 2016)

A hybrid multi-time-step framework for pore-scale and continuum-scale modeling of solute transport in porous media. - S. Karimi; K. B. Nakshatrala (CoRR, 2016)

Modeling flow in porous media with double porosity/permeability: Mathematical model, properties, and analytical solutions. - K. B. Nakshatrala; S. H. S. Joodat; R. Ballarini (CoRR, 2016)

On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method. - Maruti Kumar Mudunuru; K. B. Nakshatrala (J. Comput. Phys., 2016)

Modeling flow in porous media with double porosity/permeability: A stabilized mixed formulation, error analysis, and numerical solutions. - S. H. S. Joodat; K. B. Nakshatrala; R. Ballarini (CoRR, 2017)

Large-Scale Optimization-Based Non-negative Computational Framework for Diffusion Equations: Parallel Implementation and Performance Studies. - Justin Chang 001; Satish Karra; K. B. Nakshatrala (J. Sci. Comput., 2017)

A performance spectrum for parallel computational frameworks that solve PDEs. - Justin Chang 001; K. B. Nakshatrala; Matthew G. Knepley; S. Lennart Johnsson (Concurr. Comput. Pract. Exp., 2018)

A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model. - M. S. Joshaghani; S. H. S. Joodat; K. B. Nakshatrala (CoRR, 2018)

Global sensitivity analysis of frequency band gaps in one-dimensional phononic crystals. - W. Witarto; K. B. Nakshatrala; Y. L. Mo (CoRR, 2018)

A global sensitivity analysis and reduced order models for hydraulically-fractured horizontal wells. - Ali Rezaei; Kalyana B. Nakshatrala; Fahd Siddiqui; Birol Dindoruk; Mohammed Soliman (CoRR, 2018)

A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity. - N. K. Mapakshi; Justin Chang 001; K. B. Nakshatrala (J. Comput. Phys., 2018)

On interface conditions for flows in coupled free-porous media. - K. B. Nakshatrala; M. S. Joshaghani (CoRR, 2019)

On numerical stabilization in modeling double-diffusive viscous fingering. - M. Shabouei; K. B. Nakshatrala (CoRR, 2019)

On boundedness and growth of unsteady solutions under the double porosity/permeability model. - K. B. Nakshatrala (CoRR, 2019)

Composable block solvers for the four-field double porosity/permeability model. - M. S. Joshaghani; Justin Chang 001; K. B. Nakshatrala; Matthew G. Knepley (J. Comput. Phys., 2019)

On optimal designs using topology optimization for flow through porous media applications. - T. Phatak; K. B. Nakshatrala (CoRR, 2020)

A modeling framework for coupling plasticity with species diffusion. - M. S. Joshaghani; K. B. Nakshatrala (CoRR, 2020)

A deep learning modeling framework to capture mixing patterns in reactive-transport systems. - N. V. Jagtap; Maruti Kumar Mudunuru; K. B. Nakshatrala (CoRR, 2021)

Effect of viscous shearing stresses on optimal material designs for flow of fluids through porous media. - T. Phatak; K. B. Nakshatrala (CoRR, 2021)

Shapley values and machine learning to characterize metamaterials for seismic applications. - D. Oniz; Y. L. Mo; Kalyana B. Nakshatrala (CoRR, 2021)

How to pose material design problems for flow through porous media applications?: Sensitivity of dissipation rate to medium's permeability holds the key. - K. B. Nakshatrala (CoRR, 2021)

Modeling thermal regulation in thin vascular systems: A mathematical analysis. - Kalyana B. Nakshatrala (CoRR, 2022)

CoolPINNs: A Physics-informed Neural Network Modeling of Active Cooling in Vascular Systems. - N. V. Jagtap; Maruti Kumar Mudunuru; Kalyana B. Nakshatrala (CoRR, 2023)

Thermal regulation in thin vascular systems: A sensitivity analysis. - K. B. Nakshatrala; K. Adhikari (CoRR, 2023)

Dynamic properties of double porosity/permeability model. - K. B. Nakshatrala (CoRR, 2023)

Effect of temperature-dependent material properties on thermal regulation in microvascular composites. - K. Adhikari; J. F. Patrick; K. B. Nakshatrala (CoRR, 2024)

Closed-loop geothermal systems: Modeling and predictions. - K. Adhikari; Maruti Kumar Mudunuru; K. B. Nakshatrala (CoRR, 2024)

Flow Through Porous Media: A Hopf-Cole Transformation Approach for Modeling Pressure-Dependent Viscosity. - V. S. Maduri; K. B. Nakshatrala (CoRR, 2025)

Reactive Transport Modeling with Physics-Informed Machine Learning for Critical Minerals Applications. - K. Adhikari; Md. Lal Mamud; Maruti Kumar Mudunuru; K. B. Nakshatrala (CoRR, 2025)