The field of numerical methods for porous media and fluid-structure interactions is experiencing significant developments, driven by the need for more accurate and efficient simulations. Researchers are exploring new formulations, such as the Stokes-Brinkman-type formulation, and developing innovative methods like the Active Flux method and Hybrid High-Order methods. These advancements aim to improve the stability, convergence, and computational performance of numerical simulations, particularly in complex scenarios like shock-capturing and brittle fracture. Notable papers in this area include the Investigation of Shock-Capturing with Bound-Preserving Limiters for the Nonlinearly Stable Flux Reconstruction Method, which demonstrates the robustness and accuracy of the NSFR scheme, and the Hybrid High-Order method for the power-law Brinkman problem, which shows robustness in all regimes. Additionally, the development of GPU-accelerated packages like LevelSetPy and GeoWarp is enhancing computational efficiency and enabling faster simulations. These advancements have the potential to impact various fields, including geomechanics, bioengineering, and materials science.
Advancements in Numerical Methods for Porous Media and Fluid-Structure Interactions
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A Stokes-Brinkman-type formulation for the eigenvalue problem in porous media
Investigation of Shock-Capturing with Bound-Preserving Limiters for the Nonlinearly Stable Flux Reconstruction Method
Crack-tip field characterization in nonlinearly constituted and geometrically linear elastoporous solid containing a star-shaped crack: A finite element study
Benchmark stress tests for flow past a cylinder at higher Reynolds numbers using EMAC
GeoWarp: An automatically differentiable and GPU-accelerated implicit MPM framework for geomechanics based on NVIDIA Warp
Numerical Analysis of a Bio-Polymerization Model
Splitting Method for a Multilayered Poroelastic Solid Interacting with Stokes Flow
Three-dimensional SPH modeling of brittle fracture under hydrodynamic loading
Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators
LevelSetPy: A GPU-Accelerated Package for Hyperbolic Hamilton-Jacobi Partial Differential Equations
Discontinuous Galerkin approximation for a Stokes-Brinkman-type formulation for the eigenvalue problem in porous media
Acceleration methods for fixed point iterations
The Arrow-Hurwicz iteration for virtual element discretizations of the incompressible Navier-Stokes equations
A Hybrid High-Order method for the power-law Brinkman problem robust in all regimes