The field of fluid dynamics and related areas has seen significant developments in recent times, with a focus on improving numerical methods for simulating complex phenomena. One of the key directions is the development of high-order numerical schemes that can accurately capture the behavior of fluids and other materials in various settings. Researchers have been working on creating more efficient and stable algorithms for solving equations that govern fluid motion, heat transfer, and other related processes. Notably, there has been progress in developing energy-stable schemes, which are essential for simulating systems where energy conservation is crucial. Additionally, researchers have been exploring new approaches to handle complex interfaces, such as those found in multiphase flows, and developing methods to simulate acoustic wave propagation in different media. Some noteworthy papers in this area include the development of a semi-explicit compact fourth-order finite-difference scheme for the general acoustic wave equation, and a novel approach for simulating acoustic wave propagation across different media separated by a diffuse interface. Overall, these advances have the potential to improve our understanding and simulation of complex fluid dynamics and related phenomena, with applications in various fields such as engineering, physics, and environmental science.
Advances in Numerical Methods for Fluid Dynamics and Related Fields
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Improved error estimates for low-regularity integrators using space-time bounds
Robust superconvergence analysis of physics-preserving RMAC scheme for the Stokes and Navier--Stokes equations on non-uniform grids at high Reynolds numbers
Unconditionally Energy Stable Second Order Numerical Scheme for a Microemulsion model
A simple, fully-discrete, unconditionally energy-stable method for the two-phase Navier-Stokes Cahn-Hilliard model with arbitrary density ratios
A Semi-Explicit Compact Fourth-Order Finite-Difference Scheme for the General Acoustic Wave Equation
The Granule-In-Cell Method for Simulating Sand--Water Mixtures
Corrected Trapezoidal Rules for Near-Singular Surface Integrals Applied to 3D Interfacial Stokes Flow
High-Order Flux Splitting Schemes for the Euler Equations of Gas Dynamics
Acoustic Propagation/Refraction Through Diffuse Interface Models
Optimized Schwarz method for the Stokes-Darcy problem with generalized interface conditions
Discrete stability estimates for the pressureless Euler-Poisson-Boltzmann equations in the Quasi-Neutral limit
Improvement of fully-implicit two-phase pore-network models by employing generalized flux functions with additional throat variables
A First-Order Linear Energy Stable Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions under the Effect of Hyperbolic Relaxation
An efficient and energy-stable IMEX splitting scheme for dispersed multiphase flows