ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typically derived from the conservation laws of physics and are useful in a wide range of application areas. Applications powered by ExaHyPE can be run on a student's laptop, but are also able to exploit thousands of processor cores on state-of-the-art supercomputers. The engine is able to dynamically increase the accuracy of the simulation using adaptive mesh refinement where required. Due to the robustness and shock capturing abilities of ExaHyPE's numerical methods, users of the engine can simulate linear and non-linear hyperbolic PDEs with very high accuracy.Users can tailor the engine to their particular PDE by specifying evolved quantities, fluxes, and source terms. A complete simulation code for a new hyperbolic PDE can often be realised within a few hours -a task that, traditionally, can take weeks, months, often years for researchers starting from scratch. In this paper, we showcase ExaHyPE's workflow and capabilities through real-world scenarios from our two main application areas: seismology and astrophysics.PDEs written in first order form. The systems may contain both conservative and non-conservative terms. Solution method:ExaHyPE employs the discontinuous Galerkin (DG) method combined with explicit one-step ADER (arbitrary high-order derivative) time-stepping. An a-posteriori limiting approach is applied to the ADER-DG solution, whereby spurious solutions are discarded and recomputed with a robust, patch-based finite volume scheme. ExaHyPE uses dynamical adaptive mesh refinement to enhance the accuracy of the solution around shock waves, complex geometries, and interesting features.
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Physics-based dynamic rupture models capture the variability of earthquake slip in space and time and can account for the structural complexity inherent to subduction zones. Here we link tsunami generation, propagation, and coastal inundation with 3D earthquake dynamic rupture (DR) models initialized using a 2D seismo-thermo-mechanical geodynamic (SC) model simulating both subduction dynamics and seismic cycles. We analyze a total of 15 subduction-initialized 3D dynamic rupture-tsunami scenarios in which the tsunami source arises from the time-dependent co-seismic seafloor displacements with flat bathymetry and inundation on a linearly sloping beach. We first vary the location of the hypocenter to generate 12 distinct unilateral and bilateral propagating earthquake scenarios. Large-scale fault topography leads to localized up- or downdip propagating supershear rupture depending on hypocentral depth. Albeit dynamic earthquakes differ (rupture speed, peak slip-rate, fault slip, bimaterial effects), the effects of hypocentral depth (25–40 km) on tsunami dynamics are negligible. Lateral hypocenter variations lead to small effects such as delayed wave arrival of up to 100 s and differences in tsunami amplitude of up to 0.4 m at the coast. We next analyse inundation on a coastline with complex topo-bathymetry which increases tsunami wave amplitudes up to ≈1.5 m compared to a linearly sloping beach. Motivated by structural heterogeneity in subduction zones, we analyse a scenario with increased Poisson's ratio of ν = 0.3 which results in close to double the amount of shallow fault slip, ≈1.5 m higher vertical seafloor displacement, and a difference of up to ≈1.5 m in coastal tsunami amplitudes. Lastly, we model a dynamic rupture “tsunami earthquake” with low rupture velocity and low peak slip rates but twice as high tsunami potential energy. We triple fracture energy which again doubles the amount of shallow fault slip, but also causes a 2 m higher vertical seafloor uplift and the highest coastal tsunami amplitude (≈7.5 m) and inundation area compared to all other scenarios. Our mechanically consistent analysis for a generic megathrust setting can provide building blocks toward using physics-based dynamic rupture modeling in Probabilistic Tsunami Hazard Analysis.
We present a high-order discontinuous Galerkin (dg) solver of the compressible Navier-Stokes equations for cloud formation processes. The scheme exploits an underlying parallelized implementation of the ader-dg method with dynamic adaptive mesh refinement. We improve our method by a pde-independent general refinement criterion, based on the local total variation of the numerical solution. Our generic scheme shows competitive results for both classical cfd and stratified scenarios. While established methods use numerics tailored towards the specific simulation, our scheme works scenario independent. All together, our method can be seen as a perfect candidate for large scale cloud simulation runs on current and future super computers.
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