41 citations · 383 across the 48 of their papers we have counts for
48 papers
A Machine Learning-Enhanced Hopf-Cole Formulation for Nonlinear Gas Flow in Porous Media
V. S. Maduri, K. B. Nakshatrala
Accurate modeling of gas flow through porous media is critical for many technological applications, including reservoir performance prediction, carbon capture and sequestration, an…
Closed-loop geothermal systems: Modeling and predictions
K. Adhikari, M. K. Mudunuru, K. B. Nakshatrala
Geothermal energy is a sustainable baseload source recognized for its ability to provide clean energy on a large scale. Advanced Geothermal Systems (AGS) -- offer promising prototy…
Dynamic properties of double porosity/permeability model
K. B. Nakshatrala
Understanding fluid movement in multi-pored materials is vital for energy security and physiology. For instance, shale (a geological material) and bone (a biological material) exhi…
Thermal regulation in thin vascular systems: A sensitivity analysis
K. B. Nakshatrala, K. Adhikari
One of the ways natural and synthetic systems regulate temperature is via circulating fluids through vasculatures embedded within their bodies. Because of the flexibility and avail…
CoolPINNs: A Physics-informed Neural Network Modeling of Active Cooling in Vascular Systems
N. V. Jagtap, M. K. Mudunuru, K. B. Nakshatrala
Emerging technologies like hypersonic aircraft, space exploration vehicles, and batteries avail fluid circulation in embedded microvasculatures for efficient thermal regulation. Mo…
Modeling thermal regulation in thin vascular systems: A mathematical analysis
Kalyana B. Nakshatrala
Mimicking vascular systems in living beings, designers have realized microvascular composites to achieve thermal regulation and other functionalities, such as electromagnetic modul…
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
Recent studies have advocated using the total dissipation rate under topology optimization to realize material designs involving the flow of fluids through porous media. However, t…
Effect of viscous shearing stresses on optimal material designs for flow of fluids through porous media
T. Phatak, K. B. Nakshatrala
Topology optimization offers optimal material layouts, enabling automation in the design of devices. Given the recent advances in computer technology and additive manufacturing, to…
A deep learning modeling framework to capture mixing patterns in reactive-transport systems
N. V. Jagtap, M. K. Mudunuru, K. B. Nakshatrala
Prediction and control of chemical mixing are vital for many scientific areas such as subsurface reactive transport, climate modeling, combustion, epidemiology, and pharmacology. D…
A modeling framework for coupling plasticity with species diffusion
M. S. Joshaghani, K. B. Nakshatrala
This paper presents a modeling framework---mathematical model and computational framework---to study the response of a plastic material due to the presence and transport of a chemi…
On optimal designs using topology optimization for flow through porous media applications
T. Phatak, K. B. Nakshatrala
Topology optimization (TopOpt) is a mathematical-driven design procedure to realize optimal material architectures. This procedure is often used to automate the design of devices i…
On boundedness and growth of unsteady solutions under the double porosity/permeability model
K. B. Nakshatrala
There is a recent surge in research activities on modeling the flow of fluids in porous media with complex pore-networks. A prominent mathematical model, which describes the flow o…
On numerical stabilization in modeling double-diffusive viscous fingering
M. Shabouei, K. B. Nakshatrala
A firm understanding and control of viscous fingering (VF) and miscible displacement will be vital to a wide range of industrial, environmental, and pharmaceutical applications, su…
On interface conditions for flows in coupled free-porous media
K. B. Nakshatrala, M. S. Joshaghani
Many processes in nature (e.g., physical and biogeochemical processes in hyporheic zones, and arterial mass transport) occur near the interface of free-porous media. A firm underst…
A global sensitivity analysis and reduced order models for hydraulically-fractured horizontal wells
A. Rezaei, K. B. Nakshatrala, F. Siddiqui +2
We present a systematic global sensitivity analysis using the Sobol method which can be utilized to rank the variables that affect two quantity of interests -- pore pressure deplet…
Composable block solvers for the four-field double porosity/permeability model
M. S. Joshaghani, J. Chang, K. B. Nakshatrala +1
The objective of this paper is twofold. First, we propose two composable block solver methodologies to solve the discrete systems that arise from finite element discretizations of…
Global sensitivity analysis of frequency band gaps in one-dimensional phononic crystals
W. Witarto, K. B. Nakshatrala, Y. L. Mo
Phononic crystals have been widely employed in many engineering fields, which is due to their unique feature of frequency band gaps. For example, their capability to filter out the…
A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model
M. S. Joshaghani, S. H. S. Joodat, K. B. Nakshatrala
Modeling flow through porous media with multiple pore-networks has now become an active area of research due to recent technological endeavors like geological carbon sequestration…
A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity
N. K. Mapakshi, J. Chang, K. B. Nakshatrala
Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve the…
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
The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestra…
A performance spectrum for parallel computational frameworks that solve PDEs
J. Chang, K. B. Nakshatrala, M. G. Knepley +1
Important computational physics problems are often large-scale in nature, and it is highly desirable to have robust and high performing computational frameworks that can quickly ad…
Variational inequality approach to enforce the non-negative constraint for advection-diffusion equations
J. Chang, K. B. Nakshatrala
Predictive simulations are crucial for the success of many subsurface applications, and it is highly desirable to obtain accurate non-negative solutions for transport equations in…
Modeling flow in porous media with double porosity/permeability: Mathematical model, properties, and analytical solutions
K. B. Nakshatrala, S. H. S. Joodat, R. Ballarini
Geo-materials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of…
A hybrid multi-time-step framework for pore-scale and continuum-scale modeling of solute transport in porous media
S. Karimi, K. B. Nakshatrala
In this paper, we propose a computational framework,which is based on a domain decomposition technique, to employ both finite element method (which is a popular continuum modeling…