@article{chertock_kurganov_redle_wu_2024, title={A NEW LOCALLY DIVERGENCE-FREE PATH-CONSERVATIVE CENTRAL-UPWIND SCHEME FOR IDEAL AND SHALLOW WATER MAGNETOHYDRODYNAMICS}, volume={46}, ISSN={["1095-7197"]}, DOI={10.1137/22M1539009}, number={3}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Chertock, Alina and Kurganov, Alexander and Redle, Michael and Wu, Kailiang}, year={2024}, pages={A1998–A2024} }
 @article{chertock_kurganov_redle_zeitlin_2024, title={Locally divergence-free well-balanced path-conservative central-upwind schemes for rotating shallow water MHD}, volume={518}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2024.113300}, abstractNote={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 designed not only to maintain the divergence-free constraint of the magnetic field at the discrete level but also to satisfy the well-balanced (WB) property by exactly preserving some physically relevant steady states of the underlying system. The locally divergence-free constraint of the magnetic field is enforced by following the method recently introduced in Chertock et al. (2024) [19]: we consider a Godunov-Powell modified version of the studied system, introduce additional equations by spatially differentiating the magnetic field equations, and modify the reconstruction procedures for magnetic field variables. The WB property is ensured by implementing a flux globalization approach within the PCCU scheme, leading to a method capable of preserving both still- and moving-water equilibria exactly. In addition to provably achieving both the WB and divergence-free properties, the new method is implemented on an unstaggered grid and does not require any (approximate) Riemann problem solvers. The performance of the proposed method is demonstrated in several numerical experiments that confirms robustness, a high resolution of obtained results, and a lack of spurious oscillations.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Chertock, Alina and Kurganov, Alexander and Redle, Michael and Zeitlin, Vladimir}, year={2024}, month={Dec} }
 @article{jones_redle_kolla_plews_2021, title={A minimally invasive, efficient method for propagation of full-field uncertainty in solid dynamics}, ISSN={["1097-0207"]}, DOI={10.1002/nme.6818}, abstractNote={AbstractWe present a minimally invasive method for forward propagation of material property uncertainty to full‐field quantities of interest in solid dynamics. Full‐field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known a priori . The method, motivated by the well‐known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the evolution equations based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the driving term of the evolution equations. The implementation is model independent, storage and communication efficient, and straightforward. We demonstrate its efficiency, accuracy, scaling with dimension of the parameter space, and convergence in distribution with two problems: a quasi‐one‐dimensional bar impact, and a two material notched plate impact. For the bar impact problem, we provide an analytical solution to PDF of the solution fields for method validation. With the notched plate problem, we also demonstrate good parallel efficiency and scaling of the method.}, journal={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING}, author={Jones, Reese E. and Redle, Michael T. and Kolla, Hemanth and Plews, Julia A.}, year={2021}, month={Sep} }