The field of numerical methods for fluid dynamics and related fields is rapidly advancing, with a focus on developing innovative and efficient algorithms for solving complex problems. Recent developments have centered around improving the accuracy and stability of numerical schemes, particularly in the context of multiphase flows, porous media, and nonlinear systems. Notably, researchers are exploring new approaches to handle complex physics, such as sharp interface methods, augmented Lagrangian formulations, and structure-preserving schemes. These advancements have the potential to significantly impact various applications, including scientific simulations, engineering design, and environmental modeling. Noteworthy papers in this area include: The paper 'Sharp Collocated Projection Method for Immiscible Two-Phase Flows' which presents a novel method for solving two-phase Navier-Stokes equations with high accuracy and efficiency. The paper 'A Structure-Preserving Scheme for the Euler System with Potential Temperature Transport' which develops an all-speed, semi-implicit finite volume scheme that is asymptotic preserving and strictly positivity preserving for density and potential temperature.
Advances in Numerical Methods for Fluid Dynamics and Related Fields
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Sharp Collocated Projection Method for Immiscible Two-Phase Flows
Combining Nonlinear FETI-DP Methods and Quasi-Newton Methods using an SQP Approach
Augmented Lagrangian Solvers for Poroelasticity with Fracture Contact Mechanics
Implicit-Explicit Scheme with Multiscale Vanka Two-Grid Solver for Heterogeneous Unsaturated Poroelasticity
Structure-preserving parametric finite element methods for two-phase Stokes flow based on Lagrange multiplier approaches
Adaptive time-domain boundary element methods for the wave equation with Neumann boundary conditions
Porous Convection in the Discrete Exterior Calculus with Geometric Multigrid
Some semi-decoupled algorithms with optimal convergence for a four-field linear thermo-poroelastic model
A convergence proof for a finite element discretization of Chorin's projection method of the incompressible Navier-Stokes equations
Convergence analysis of the dynamically regularized Lagrange multiplier method for the incompressible Navier-Stokes equations
A well-balanced gas-kinetic scheme with adaptive mesh refinement for shallow water equations
Semi-discrete Active Flux as a Petrov-Galerkin method
Error Estimation for Adaptive Mesh Refinement in Droplet Simulations
A Structure-Preserving Scheme for the Euler System with Potential Temperature Transport
Exponential decay of the discrete energy for the wave-wave coupled system
Weighted finite difference methods for the semiclassical nonlinear Schr\"odinger equation with multiphase oscillatory initial data