A second-order time-accurate implicit finite volume method with exact two-phase Riemann problems for compressible multi-phase fluid and fluid-structure problems. - Alex Main; Charbel Farhat (J. Comput. Phys., 2014)

A stable partitioned FSI algorithm for incompressible flow and deforming beams. - Longfei Li; William D. Henshaw; Jeffrey W. Banks; Donald W. Schwendeman; Alex Main (J. Comput. Phys., 2016)

An enhanced FIVER method for multi-material flow problems with second-order convergence rate. - Alex Main; Xianyi Zeng; Philip Avery; Charbel Farhat (J. Comput. Phys., 2017)

The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems. - Alex Main; Guglielmo Scovazzi (J. Comput. Phys., 2018)

The shifted boundary method for embedded domain computations. Part II: Linear advection-diffusion and incompressible Navier-Stokes equations. - Alex Main; Guglielmo Scovazzi (J. Comput. Phys., 2018)

The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows. - Ting Song; Alex Main; Guglielmo Scovazzi; Mario Ricchiuto (J. Comput. Phys., 2018)

Dual-scale Galerkin methods for Darcy flow. - Guoyin Wang; Guglielmo Scovazzi; Léo Nouveau; Christopher E. Kees; Simone Rossi 003; Oriol Colomés; Alex Main (J. Comput. Phys., 2018)

A weighted Shifted Boundary Method for free surface flow problems. - Oriol Colomés; Alex Main; Léo Nouveau; Guglielmo Scovazzi (J. Comput. Phys., 2021)

A weighted shifted boundary method for immersed moving boundary simulations of Stokes' flow. - Danjie Xu; Oriol Colomés; Alex Main; Kangan Li; Nabil M. Atallah; Nabil Abboud; Guglielmo Scovazzi (J. Comput. Phys., 2024)