The article describes direct numerical simulations using an Euler–Lagrange
approach with an immersed-boundary method to resolve the geometry and trajectory
of particles moving in a flow. The presentation focuses on own work
of the authors and discusses elements of physical and numerical modeling in
some detail, together with three areas of application: microfluidic transport
of spherical and nonspherical particles in curved ducts, flows with bubbles at
different void fraction ranging from single bubbles to dense particle clusters,
some also subjected to electro-magnetic forces, and bedload sediment transport
with spherical and nonspherical particles. These applications with their specific
requirements for numerical modeling illustrate the versatility of the approach
and provide condensed information about main findings.