229 citations · 396 across the 31 of their papers we have counts for
33 papers
Fifth-Order Well-Balanced Path-Conservative A-WENO Scheme for the Ripa Model
Yan-Ping Qiu, Zhen Gao, Alexander Kurganov +2
In this work, we introduce a fifth-order well-balanced (WB) path-conservative A-WENO scheme with the central-upwind numerical fluxes (PCCU-5) for the Ripa model. The proposed schem…
Adaptive Artificial Anti-Diffusion Methods for Hyperbolic Systems of Conservation Laws
Shaoshuai Chu, Igor Kliakhandler, Alexander Kurganov
We introduce new adaptive artificial anti-diffusion (AAAD) methods for one- and two-dimensional hyperbolic systems of conservation laws. The key idea is to reduce the amount of num…
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…
New Low-Dissipation Central-Upwind Schemes. Part II
Shaoshuai Chu, Alexander Kurganov, Ruixiao Xin
The low-dissipation central-upwind (LDCU) schemes have been recently introduced in [A. Kurganov and R. Xin, J. Sci. Comput., 96 (2023), Paper No. 56] as a modification of the centr…
On the Gelfand Problem and Viscosity Matrices for Two-Dimensional Hyperbolic Systems of Conservation Laws
Shaoshuai Chu, Igor Kliakhandler, Alexander Kurganov
We present counter-intuitive examples of a viscous regularizations of a two-dimensional strictly hyperbolic system of conservation laws. The regularizations are obtained using two…
Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes
Shaoshuai Chu, Michael Herty, Alexander Kurganov
We introduce local characteristic decomposition based path-conservative central-upwind schemes for (nonconservative) hyperbolic systems of balance laws. The proposed schemes are ma…
Bound-Preserving Framework for Central-Upwind Schemes for General Hyperbolic Conservation Laws
Shumo Cui, Alexander Kurganov, Kailiang Wu
Central-upwind (CU) schemes are Riemann-problem-solver-free finite-volume methods widely applied to a variety of hyperbolic systems of PDEs. Exact solutions of these systems typica…
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…
Low-Dissipation Central-Upwind Schemes for Compressible Multifluids
Shaoshuai Chu, Alexander Kurganov, Ruixiao Xin
We introduce second-order low-dissipation (LD) path-conservative central-upwind (PCCU) schemes for the one- (1-D) and two-dimensional (2-D) multifluid systems, whose components are…
New Adaptive Low-Dissipation Central-Upwind Schemes
Shaoshuai Chu, Alexander Kurganov
We introduce new second-order adaptive low-dissipation central-upwind (LDCU) schemes for the one- and two-dimensional hyperbolic systems of conservation laws. The new adaptive LDCU…
Experimental Convergence Rate Study for Three Shock-Capturing Schemes and Development of Highly Accurate Combined Schemes
Shaoshuai Chu, Olyana A. Kovyrkina, Alexander Kurganov +1
We study experimental convergence rates of three shock-capturing schemes for hyperbolic systems of conservation laws: the second-order central-upwind (CU) scheme, the third-order R…
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…