Efficient High-Order Discretizations for Computational Fluid Dynamics

High-order numerical methods promise improved accuracy for computational fluid dynamics, but their real value depends on careful choices in formulation, algorithms, and implementation. Efficient High-Order Discretizations for Computational Fluid Dynamics brings those questions together through a focused examination of discontinuous Galerkin (DG) methods—from their mathematical foundations to their use in demanding flow simulations.

Edited by Martin Kronbichler and Per-Olof Persson, this research-oriented volume links finite-element and finite-volume ideas to explain how DG methods represent solutions across mesh elements and exchange information between them. Its seven chapters move from core principles to computational practice, making the book useful for readers who want to understand not only how these methods are constructed, but also the challenges involved in using them efficiently.

From DG foundations to working algorithms

The opening chapters introduce the derivation, stability, and convergence properties of discontinuous Galerkin schemes, then examine their high-performance implementation. Later contributions address robust nodal DG spectral-element methods for compressible Navier–Stokes equations, p-multigrid approaches for compressible flows, time integration and implicit solvers, and the hybridizable discontinuous Galerkin method.

Why implementation matters

High-order discretizations can reduce dispersion and dissipation errors in suitable simulations, while their performance depends on how the numerical method is matched to hardware and computational demands. The chapters consider these practical trade-offs alongside the theory, including efficient computation and strategies for solving the systems that arise in fluid-flow applications.

A research-led view of computational fluid dynamics

Rather than treating DG as a single recipe, the volume presents a range of methods and research directions. Its concluding engineering perspective also considers the challenges that remain for high-order approaches in practical simulation.

Who may find this volume useful?

The book is primarily suited to doctoral students and researchers in engineering, applied mathematics, physics, and high-performance computing. Practicing computational engineers looking for a deeper overview of DG methods, modern algorithms, and their implementation may also find it relevant.