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.