204 citations · 362 across the 25 of their papers we have counts for
24 papers · 1 filter
An Asymptotic-Preserving Dual Formulation Finite-Volume Method for the Thermal Rotating Shallow Water Equations
Alina Chertock, Alexander Kurganov, Lorenzo Micalizzi +1
We propose a new second-order asymptotic-preserving (AP) dual formulation finite-volume (DF-FV) method for the thermal rotating shallow water (TRSW) equations. The TRSW system mode…
A New Asymptotic-Preserving Dual Formulation Finite-Volume Method for the Compressible Euler Equations
Alina Chertock, Smadar Karni, Alexander Kurganov +1
The paper focuses on the development of numerical methods for the compressible Euler equations. It is well-known that if the Mach number is small, the system becomes stiff and henc…
New Adaptive Numerical Methods Based on Dual Formulation of Hyperbolic Conservation Laws
Alina Chertock, Qingcheng Fu, Alexander Kurganov +1
In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solu…
Numerical Study of Random Kelvin-Helmholtz Instability
Alina Chertock, Michael Herty, Arsen S. Iskhakov +3
In this paper, we study random dissipative weak solutions of the compressible Euler equations in the Kelvin-Helmholtz (KH) instability. Motivated by the fact that weak entropy solu…
Uncertainty Quantification in Forward Problems: Balancing Accuracy and Robustness Using CWENO Interpolations
Alina Chertock, Arsen S. Iskhakov, Alexander Kurganov
In this paper, we study uncertainty quantification (UQ) in forward problems. Our objective is to construct accurate and robust surrogate models by incorporating the seventh-order c…
New Smoothness Indicator Within an Active Flux Framework
Alina Chertock, Alexander Kurganov, Lorenzo Micalizzi
In this work, we introduce a new smoothness indicator (SI), which is capable of detecting ``rough'' parts of the solutions computed by active flux (AF) methods for hyperbolic (syst…
Dual Formulation Finite-Volume Methods on Overlapping Meshes for Hyperbolic Conservation Laws
Rémi Abgrall, Alina Chertock, Alexander Kurganov +1
In this work, we introduce new second-order schemes for one- and two-dimensional hyperbolic systems of conservation laws. Following an approach recently proposed in [{\sc R. Abgral…
CWENO Interpolation for Non-Oscillatory Stochastic Collocation in Uncertainty Quantification Problems
Alina Chertock, Arsen S. Iskhakov, Anna Iskhakova +1
Uncertainty quantification (UQ) in mathematical models is essential for accurately predicting system behavior under variability. This study provides guidance on method selection fo…
A Hybrid Finite-Difference-Particle Method for Chemotaxis Models
Alina Chertock, Shumo Cui, Alexander Kurganov +1
Chemotaxis systems play a crucial role in modeling the dynamics of bacterial and cellular behaviors, including propagation, aggregation, and pattern formation, all under the influe…
Spline-Based Stochastic Collocation Methods for Uncertainty Quantification in Nonlinear Hyperbolic PDEs
Alina Chertock, Arsen S. Iskhakov, Safa Janajra +1
In this paper, we study the stochastic collocation (SC) methods for uncertainty quantification (UQ) in hyperbolic systems of nonlinear partial differential equations (PDEs). In the…
Divergence-Free Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Rotating Shallow Water Magnetohydrodynamics
Alina Chertock, Alexander Kurganov, Michael Redle +1
We develop a new second-order flux globalization based path-conservative central-upwind (PCCU) scheme for rotating shallow water magnetohydrodynamic equations. The new scheme is de…
New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
Alina Chertock, Michael Herty, Arsen S. Iskhakov +3
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realize…
Denoising Convolution Algorithms and Applications to SAR Signal Processing
Alina Chertock, Chris Leonard, Semyon Tsynkov +1
Convolutions are one of the most important operations in signal processing. They often involve large arrays and require significant computing time. Moreover, in practice, the signa…
A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics
Alina Chertock, Alexander Kurganov, Michael Redle +1
We develop a new second-order unstaggered path-conservative central-upwind (PCCU) scheme for ideal and shallow water magnetohydrodynamics (MHD) equations. The new scheme possesses…
Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator
Alina Chertock, Shaoshuai Chu, Alexander Kurganov
We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed…
A Diffuse-Domain Based Numerical Method for a Chemotaxis-Fluid Model
Chenxi Wang, Alina Chertock, Shumo Cui +2
In this paper, we consider a coupled chemotaxis-fluid system that models self-organized collective behavior of oxytactic bacteria in a sessile drop. This model describes the biolog…
Local Characteristic Decomposition Based Central-Upwind Scheme
Alina Chertock, Shaoshuai Chu, Michael Herty +2
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the…
Stochastic Galerkin method for cloud simulation. Part II: a fully random Navier-Stokes-cloud model
A. Chertock, A. Kurganov, M. Lukáčová-Medviďová +2
This paper is a continuation of the work presented in [Chertock et al., Math. Cli. Weather Forecast. 5, 1 (2019), 65--106]. We study uncertainty propagation in warm cloud dynamics…
Finding the Shape of Lacunae of the Wave Equation Using Artificial Neural Networks
Alina Chertock, Christopher Leonard, Semyon Tsynkov
We apply a fully connected neural network to determine the shape of the lacunae in the solutions of the wave equation. Lacunae are the regions of quietness behind the trailing fron…
On a hybrid continuum-kinetic model for complex fluids
A. Chertock, P. Degond, G. Dimarco +2
In the present work, we first introduce a general framework for modelling complex multiscale fluids and then focus on the derivation and analysis of a new hybrid continuum-kinetic…
Stochastic Galerkin method for cloud simulation
A. Chertock, A. Kurganov, M. Lukáčová-Medviďová +2
We develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertaint…
Well-Balanced Schemes for the Euler Equations with Gravitation: Conservative Formulation Using Global Fluxes
Alina Chertock, Shumo Cui, Alexander Kurganov +2
We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purel…
An asymptotic preserving scheme for kinetic models with singular limit
Alina Chertock, Changhui Tan, Bokai Yan
We propose a new class of asymptotic preserving schemes to solve kinetic equations with mono-kinetic singular limit. The main idea to deal with the singularity is to transform the…
A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
José A. Carrillo, Alina Chertock, Yanghong Huang
We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate comp…