A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Convergence to steady state solutions of the Euler equations on unstructured grids with limiters
Journal of Computational Physics
The NURBS book
Application of generalized wavelets: an adaptive multiresolution scheme
Journal of Computational and Applied Mathematics
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I
SIAM Journal on Scientific Computing
Average-state Jacobians and implicit methods for compressible viscous and turbulent flows
Journal of Computational Physics
Multiresolution Based on Weighted Averages of the Hat Function I: Linear Reconstruction Techniques
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Multiresolution schemes on triangles for scalar conservation laws
Journal of Computational Physics
Point Value Multiscale Algorithms for 2D Compressible Flows
SIAM Journal on Scientific Computing
Adifor 2.0: Automatic Differentiation of Fortran 77 Programs
IEEE Computational Science & Engineering
Fully adaptive multiresolution finite volume schemes for conservation laws
Mathematics of Computation
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A conservative fully adaptive multiresolution algorithm for parabolic PDEs
Journal of Computational Physics
Shock-Vortex Interactions at High Mach Numbers
Journal of Scientific Computing
Grid Generation Methods
Fully Adaptive Multiscale Schemes for Conservation Laws Employing Locally Varying Time Stepping
Journal of Scientific Computing
Application of B-spline techniques to the modeling of airplane wings and numerical grid generation
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
Adaptive Timestep Control for Nonstationary Solutions of the Euler Equations
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
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, 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 which again is to support the adaptation concepts. We conclude with numerical examples of realistic applications demonstrating different features of the solver.