Active Flux Methods: Developments and Applications

Workshop Title: Active Flux Methods: Development and Applications

Dates: December 6-8, 2025

Description:

This workshop will bring together researchers working on the development, analysis, and application of Active Flux (AF) methods—a class of numerical schemes for hyperbolic partial differential equations that combine high-order accuracy, robustness, and conservation with novel reconstruction strategies. Originating as an alternative to classical finite volume and discontinuous Galerkin methods, AF schemes utilize pointwise degrees of freedom at cell interfaces, evolved through exact or approximate evolution operators, which yield significant advantages in capturing wave phenomena and reducing numerical dissipation.

The goals of the workshop are:

• To survey recent advances in the design and analysis of AF methods, including their extensions to systems with source terms, nonconservative structures, and stiff regimes.
• To discuss new strategies for reconstruction, stability enhancement, and adaptivity within the AF framework.
• To showcase emerging applications of AF methods in fields such as fluid dynamics, magnetohydrodynamics, plasma physics, shallow water, and others.
• To foster interdisciplinary collaboration between developers of numerical methods and researchers working on complex physical systems where AF schemes can provide tangible benefits.

Topics may include (but are not limited to):

• Active Flux methods for linear and nonlinear hyperbolic systems
• Extensions to multidimensional, nonconservative, or coupled systems
• Structure-preserving and asymptotic-preserving formulations
• Treatment of boundary conditions and complex geometries
• Comparison with traditional high-order methods
• Applications to compressible flows, low Mach number regimes, and multiphysics models
• Implementation strategies and computational efficiency

The workshop will include invited talks, contributed presentations, and free discussions to foster the exchange of ideas and explore future directions in this rapidly evolving field.

The list of Invited Speakers:

Lorenzo Micalizzi, NC State Univerity, USA

Philip Roe, University of Michigan, USA

Huazhong Tang, Peking University, China

Tao Tang, Nanfang College Guangzhou, China

Eleuterio Toro, University of Trento, Italy

Kailiang Wu, SUSTech, China

Feng Xiao, Institute of Science Tokyo, Japan

Tao Xiong, USTC, China

Nan Zhang, SUSTech, China