In the field of computational fluid dynamics, many applications of practical interest require
the use of robust discretization techniques equipped with adaptive control mechanisms for …

The remap phase in arbitrary Lagrangian–Eulerian (ALE) hydrodynamics involves the
transfer of field quantities defined on a post‐Lagrangian mesh to some new mesh, usually …

Many mathematical models of continuum mechanics are derived from integral conservation
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …

In this paper, we present a collection of algorithmic tools for constraining high-order
discontinuous Galerkin (DG) approximations to hyperbolic conservation laws. We begin with …

Computational fluid dynamics (CFD) is the art of solving partial differential equations that
model the motion of fluids, as well as mass and heat transfer phenomena. This book …

Many mathematical models of computational fluid dynamics involve transport of conserved
quantities, which must lie in a certain range to be physically meaningful. The analytical or …

This work addresses the design of failsafe flux limiters for systems of conserved quantities
and derived variables in numerical schemes for the equations of gas dynamics. Building on …

We develop a fast, efficient and accurate optimization-based algorithm for the high-order
conservative and local-bound preserving remap (constrained interpolation) of a scalar …

This paper examines the application of optimization and control ideas to the formulation of
feature-preserving numerical methods, with particular emphasis on the conservative and …

To ensure preservation of local or global bounds for numerical solutions of conservation
laws, we constrain a baseline finite element discretization using optimization-based (OB) …