Liu G.R., Mao Zirui. Gradient Smoothing Methods with Programming: Applications to Fluids and Landslides

World Scientific Publishing, 2024. — 288 p. — (Frontier Research in Computation and Mechanics of Materials and Biology. Volume 5). — ISBN 978-981-128-000-9.This unique compendium presents the Gradient Smoothing Methods (GSMs), as a general solver for linear and nonlinear PDEs (Partial Differential Equations) with a focus on fluids and flowing solids.The volume introduces the basic concepts and theories of the gradient smoothing technique used in the GSMs. Formulations for both Eulerian-GSM and Lagrangian-GSM are presented. The key ingredients of GSMs and its effectiveness in solving challenging fluid/solid flow problems with complex geometries are then discussed.Applications of GSM are highlighted, including compressible and incompressible flows, hydrodynamics with flexible free surface, and flowing solids with material strength and large deformation in geotechnical engineering, in particular, landslide simulations.In-house MatLAB codes are provided for both Eulerian and Lagrangian GSMs, along with detailed descriptions. More efficient FORTRAN source codes for solving complex engineering problems are also available on Github.Introduction
Theory for Gradient Smoothing Methods
Eulerian GSM for Solving Poisson Equation
Eulerian GSM for Compressible Flows
Eulerian GSM for Incompressible Flows
Theory and Formulation for Lagrangian GSM
L-GSM for Incompressible Hydrodynamics
L-GSM for Granular Flows in Geotechnical Engineering
Programming with GSMs and Source Codes