Finite Volume

Finite volume methods are numerical techniques for solving partial differential equations (PDEs), primarily by discretizing the problem domain into control volumes and applying conservation principles to each. Current research emphasizes improving efficiency and accuracy through techniques like domain decomposition with Schwarz methods and incorporating machine learning for subgrid modeling and faster simulations. These advancements are crucial for tackling computationally expensive problems in diverse fields such as fluid dynamics, reservoir management, and tsunami modeling, enabling more accurate and timely predictions. The integration of machine learning with established finite volume methods is a particularly active area, aiming to improve both speed and accuracy.