This book is intended primarily as a textbook for second-year undergraduate students in
mathematics, mathematical physics, and engineering. The book is designed as a first …

The application of the Immersed Boundary (IB) method to simulate incompressible, turbulent
flows around complex configurations is illustrated; the IB is based on the use of non-body …

Reacting flow simulations for combustion applications require extensive computing
capabilities. Leveraging the AMReX library, the Pele suite of combustion simulation tools …

An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in
complex geometries is presented. A boundary condition is enforced through a ghost cell …

A Cartesian grid method has been developed for simulating two-dimensional unsteady,
viscous, incompressible flows with complex immersed boundaries. A finite-volume method …

We present a numerical method using the level set approach for solving incompressible two-
phase flow with surface tension. In the level set approach, the free surface is represented as …

We present a numerical method for solving Poisson's equation, with variable coefficients
and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite …

A Cartesian grid method for computing flows with complex immersed, moving boundaries is
presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are …

A second-order accurate interface tracking method for the solution of incompressible Stokes
flow problems with moving interfaces on a uniform Cartesian grid is presented. The interface …

We perform numerical simulations of a disc–planet system using various grid-based and
smoothed particle hydrodynamics (SPH) codes. The tests are run for a simple setup where …