A C++ computational laboratory for adaptive numerical methods targeting hyperbolic balance laws, enabling rapid prototyping and testing of new algorithms and mathematical concepts. Developed at the IGPM, RWTH Aachen.
Read the paper →Characteristic Features
- Strong-stability-preserving Runge-Kutta discontinuous Galerkin (RKDG) schemes
- Adaptive grid refinement via multiresolution analysis
- Local projection limiting for stabilization near discontinuities
- Viscous flux handling via the Bassi-Rebay (BR2) method
- Path-conservative DG for non-conservative products
- Well-balanced formulations for shallow water systems
- MPI-based distributed memory parallelization with load rebalancing
- Modular C++ architecture with compile-time policy selection
Application Areas
- Compressible Euler equations
- Compressible Navier-Stokes equations
- Shallow water equations with bottom topography
- Multi-phase flows with non-conservative terms
- Traffic flow models
- Biomedical flow applications
- Continuum physics and manufacturing processes
- Parameter-dependent problems and uncertainty quantification (UQ)
Simulations & Results
▶ VIDEO
Wave Interaction
▶ VIDEO
Double Mach Reflection
▶ VIDEO
Air Bubble Impacting Plastic Wall
▶ VIDEO
Dam Break – Flooded City
▶ VIDEO
Tsunami Run-Up
Malpasset Dam Break
Shock-Boundary Layer Interaction
Turbulent Channel Flow
Uncertainty Quantification
A Posteriori Error Estimates
Publications
- MultiWave: A computational lab for adaptive numerical methods approximating hyperbolic balance laws arXiv preprint, 2025 Link →
- Discontinuous Galerkin schemes for multi-dimensional coupled hyperbolic systems arXiv preprint, 2026 Link →
- Multiresolution-based grid adaptation for the compression of ERA5 meteorological reanalysis data in MPTRAC v2.7 Preprint, 2026 Link →
- Numerical boundary control of multi-dimensional hyperbolic equations Mathematical Control and Related Fields, 2025 Link →
- A-posteriori error estimates for systems of hyperbolic conservation laws via computing negative norms of local residuals IMA Journal of Numerical Analysis, 2025 Link →
- Coupled generalized Riemann problems for the Euler equations Journal of Computational and Applied Mathematics, 2025 Link →
- Multiresolution analysis for stochastic hyperbolic conservation laws IMA Journal of Numerical Analysis, 44(1):536–575, 2024 Link →
- A novel multilevel approach for the efficient computation of random hyperbolic conservation laws Multiscale, Nonlinear and Adaptive Approximation II, Springer, 327–346, 2024 Link →
- Model adaptation for hyperbolic balance laws HYP2022 Proceedings, Springer, 2024 Link →
- Radially symmetric solutions of the ultra-relativistic Euler equations in several space dimensions Journal of Computational Physics, 518:113330, 2024 Link →
- Multiresolution-based grid adaptation for hyperbolic conservation laws with uncertain initial data PhD thesis, RWTH Aachen University, 2023 Link →
- Higher-dimensional deterministic approach for conservation laws with random initial data HYP2022 Proceedings, Springer, 111–120, 2022 Link →
- A wavelet-free approach for multiresolution-based grid adaptation for conservation laws Communications on Applied Mathematics and Computation, 4:1–35, 2021 Link →
- Coupling of two hyperbolic systems by solving half-Riemann problems Mathematical Modeling, Simulation and Optimization for Power Engineering, Springer, 285–302, 2021 Link →
- Analysis and numerical methods for the coupling of hyperbolic problems PhD thesis, RWTH Aachen University, 2020 Link →
- Multiwavelet-based mesh adaptivity with discontinuous Galerkin schemes: exploring 2D shallow water problems Advances in Water Resources, 138:103559, 2020 Link →
- Hyperbolic stochastic Galerkin formulation for the p-system Journal of Computational Physics, 395:186–204, 2019 Link →
- An adaptive multiresolution discontinuous Galerkin scheme for conservation laws PhD thesis, RWTH Aachen University, 2017 Link →
- Adaptive multiresolution discontinuous Galerkin schemes for conservation laws: multi-dimensional case Computational and Applied Mathematics, 35:321–349, 2016 Link →
- Multiwavelet-based grid adaptation with discontinuous Galerkin schemes for shallow water equations Journal of Computational Physics, 301:265–288, 2015 Link →
- A high-order discontinuous Galerkin discretization with multiwavelet-based grid adaptation for compressible flows Journal of Scientific Computing, 62:25–52, 2015 Link →
- Adaptive multiresolution discontinuous Galerkin schemes for conservation laws Mathematics of Computation, 83(285):113–151, 2014 Link →