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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.
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