H-Adaptive Multiscale Schemes for the Compressible Navier-Stokes Equations — Polyhedral Discretization, Data Compression and Mesh Generation

Abstract

In this paper we present the main conceptual ingredients and the current state of development of the new solver QUADFLOW for large scale simulations of compressible fluid flow and fluid-structure interaction. In order to keep the size of the discrete problems at every stage as small as possible for any given target accuracy, we employ a multiresolution adaptation strategy that will be described in the first part of the paper. In the second part we outline a new mesh generation concept that is to support the adaptive concepts as well as possible. A key idea is to understand meshes as parametric mappings determined by possibly few control points as opposed to store each mesh cell separately. Finally, we present a finite volume discretization along with suitable data structures which again is to support the adaptation concepts. We conclude with numerical examples of realistic applications demonstrating different features of the solver.

Parallel and Adaptive Methods for Fluid-Structure-Interactions

“…The property which we impose on the coupling is that the discrete fluid-structure system satisfies the same energy balance as the continuous system, see (6) below. Obviously this is an important property.…”

“…In order to be able to meet the requirements of highly accurate nonstationary simulations based on the full Navier Stokes equations as a fluid model a new fully adaptive solver Quadflow has been developed [6,7]. More specifically, it has been designed to handle (i) unstructured grids composed of polygonal(2D)/polyhedral(3D) elements [5] and (ii) block-structured grids where in each block the grid is determined by local evaluation of B-Spline mappings [17].…”

“…The dotted line shows the λ -value for which each coupling scheme predicts the bifurcation as ∆t → 0. The method denoted as FPI, solves in each time step the discrete system that satisfies (6), by a fixed-point iteration, which iterates the loose coupling until a convergence criterion is met. On average this happens after two iterations.…”

Numbering techniques for preconditioners in iterative solvers for compressible flows

“…For the numerical simulation of the compressible Euler equations we use the software package QUADFLOW, which is currently under development at Aachen University, cf. [5,9,10,11,39]. We briefly describe a few main features of this solver.…”

“…A method of this class has been implemented in the QUADFLOW package, which is an adaptive multiscale finite volume solver for stationary and instationary compressible flow computations. Descriptions of this solver are given in [5,9,10,11,39]. For the linearization we use a standard (approximate) Newton method.…”