41 citations · 383 across the 48 of their papers we have counts for
33 papers · 1 filter
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…
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…
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…
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…
Large-scale Optimization-based Non-negative Computational Framework for Diffusion Equations: Parallel Implementation and Performance Studies
J. Chang, S. Karra, K. B. Nakshatrala
It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does…
On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method
M. K. Mudunuru, K. B. Nakshatrala
We present a robust computational framework for advective-diffusive-reactive systems that satisfies maximum principles, the non-negative constraint, and element-wise species balanc…
Do current lattice Boltzmann methods for diffusion and diffusion-type equations respect maximum principles and the non-negative constraint?
S. Karimi, K. B. Nakshatrala
The lattice Boltzmann method (LBM) has established itself as a valid numerical method in computational fluid dynamics. Recently, multiple-relaxation-time LBM has been proposed to s…
On mesh restrictions to satisfy comparison principles, maximum principles, and the non-negative constraint: Recent developments and new results
M. K. Mudunuru, K. B. Nakshatrala
This paper concerns with mesh restrictions that are needed to satisfy several important mathematical properties -- maximum principles, comparison principles, and the non-negative c…
Mechanics-based solution verification for porous media models
M. Shabouei, K. B. Nakshatrala
This paper presents a new approach to verify accuracy of computational simulations. We develop mathematical theorems which can serve as robust a posteriori error estimation techniq…
A monolithic multi-time-step computational framework for first-order transient systems with disparate scales
S. Karimi, K. B. Nakshatrala
Developing robust simulation tools for problems involving multiple mathematical scales has been a subject of great interest in computational mathematics and engineering. A desirabl…
Modification to Darcy model for high pressure and high velocity applications and associated mixed finite element formulations
J. Chang, K. B. Nakshatrala
The Darcy model is based on a plethora of assumptions. One of the most important assumptions is that the Darcy model assumes the drag coefficient to be constant. However, there is…
On multi-time-step monolithic coupling algorithms for elastodynamics
S. Karimi, K. B. Nakshatrala
We present a way of constructing multi-time-step monolithic coupling methods for elastodynamics. The governing equations for constrained multiple subdomains are written in dual Sch…
A framework for coupling flow and deformation of the porous solid
D. Z. Turner, K. B. Nakshatrala, M. J. Martinez
In this paper, we consider the flow of an incompressible fluid in a deformable porous solid. We present a mathematical model using the framework offered by the theory of interactin…
A numerical framework for diffusion-controlled bimolecular-reactive systems to enforce maximum principles and non-negative constraint
K. B. Nakshatrala, M. K. Mudunuru, A. J. Valocchi
We present a novel computational framework for diffusive-reactive systems that satisfies the non-negative constraint and maximum principles on general computational grids. The gove…
A numerical methodology for enforcing maximum principles and the non-negative constraint for transient diffusion equations
K. B. Nakshatrala, H. Nagarajan, M. Shabouei
Transient diffusion equations arise in many branches of engineering and applied sciences (e.g., heat transfer and mass transfer), and are parabolic partial differential equations.…
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
The main aim of this paper is to document the performance of -refinement with respect to maximum principles and the non-negative constraint. The model problem is (steady-state)…
A framework for coupled deformation-diffusion analysis with application to degradation/healing
M. K. Mudunuru, K. B. Nakshatrala
This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model…