Common validation and verification test cases for compressible flow solvers are only one- or two-dimensional. Such flows, however, are inherently three-dimensional. The provided data contains simulation results of genuine three-dimensional Riemann problems computed with the open-source compressible flow solver ALPACA. The problems are designed so that each octant's constant initial state connects two neighboring states by only one elementary wave each. Thereby, initial conditions are chosen to induce three-dimensional effects. Furthermore, the cases are designed to trigger common shortcomings of compressible flow solvers, such as spurious pressure oscillations, unphysical symmetry breaking, or the onset of shock disturbances. The cases were simulated using a finite-volume scheme with HLLC and Roe Riemann solvers and fifth-order WENO reconstruction. The simulations were conducted on over 300 cores of a compute cluster. Besides the raw binary flow field data, input files are provided next to post-processing scripts and the visualizations obtained by them. The provided files ease setting up and simulating the respective cases with different solvers and allow quantitative comparisons of the obtained results.

Numerical simulation is a well -established way of analyzing compressible flows. Due to high computational demands of solvers for such flow problems, their verification is typically limited to two-dimensional (2D) cases. However, 2D simulations suppress fundamental three-dimensional (3D) aspects of the flow evolution in (compressible) turbulent flows or shock -bubble and shock -drop interactions. With increase of computational power, 3D simulations become more feasible for routine analyses. The verification of 3D simulation frameworks is often limited to transformations of lower dimensional test cases in the 3D space. There is a lack of strictly 3D reference test cases for gas dynamics. In this work, we present a set of genuine 3D Riemann problems in order to validate and verify numerical solvers for compressible flows. The problems are designed such that each octant's constant initial data connects two neighboring states by an elementary wave only. The problem design is inspired by well -established 2D Riemann problems most prominently posted by Lax and Liu (1998). In contrast to the twenty published 2D cases, more than 300 distinct combinations can be found in 3D. We provide example solutions for the particularly interesting ones of these case combinations and show how the cases help to expose shortcomings of numerical solvers. We provide reference data from computations with an open -source compressible multiresolution flow solver. For the reference solutions, we employ the Harten-Laxvan Leer contact (HLLC) Riemann solver and a weighted essentially non -oscillatory (WENO) reconstruction stencil of fifth order. The reference solutions use an effective resolution of one billion cells. We additionally make the full compute pipeline of this work publicly available, so interested researchers may reproduce and extend the current work.

We present a hybrid reconstruction scheme for compressible multiphase flows governed by the five-equation model with surface tension and molecular viscosity. The Godunov-type method utilizes a fifth-order incremental stencil weighted essential non-oscillatory (WENO5IS) scheme to resolve flow structures in each component, while the Tangent of Hyperbola for INterface Capturing (THINC) maintains sharp fluid interfaces. Supplemented with positivity-and boundedness-preserving limiting procedures, the scheme exhibits a high level of robustness for multiphase flow problems with strong compressibility and large acoustic impedance mismatch. One-and two-dimensional benchmark cases demonstrate the efficiency and accuracy of interface-sharpening, and the high resolution capability for each fluid component. Numerical tests under extreme conditions corroborate the excellent robustness, and simulations with surface tension and viscosity also exhibit the versatility of the proposed approach.

Most technological advancements in medicine, process and energy engineering, life and food science, mobility and environmental engineering involve mastering fluid mechanical effects. In particular, compressible flow physics including shockwaves and phase‐interface interactions exhibit multi‐scale phenomena spanning several orders of magnitude upwards from nanometer and nanosecond time scales. Clearly, detailed analysis of such effects is impossible by means of experimental techniques. On the contrary, numerical modeling and simulations allow to capture the aforementioned mechanisms and provide non‐invasive access to any quantity of interest. Yet, the complex fluid physics require powerful computational methods utilizing recent advancements for high‐order schemes. In this work, we provide an overview on latest high‐order low‐dissipation schemes using level sets to model discontinuous phase‐interface interactions.

In this short note, we highlight the sensitivity of the HLL-type Riemann solver with respect to the choice of signal speed estimates and demonstrate a major deficiency of the arithmetic-average estimate. The investigation of two essential Riemann problems and a classical bow shock simulation reveals that inherent inconsistencies of the arithmetic-average estimate may lead to unexpected behavior and erroneous results.

The purpose of this paper is twofold. First, the application of high-order methods in combination with the popular HLLC Riemann solver demonstrates that the grid-aligned shock instability can strongly affect simulation results when the grid resolution is increased. Beyond the well-documented two-dimensional behavior, the problem is particularly troublesome with three-dimensional simulations. Hence, there is a need for shock-stable modifications of HLLC-type solvers for high-speed flow simulations. Second, the paper provides a stabilization of the popular HLLC flux based on a recently proposed mechanism for grid aligned-shock instabilities Fleischmann et al. (2020) [8]. The instability was found to be triggered by an inappropriate scaling of acoustic and advection dissipation for local low Mach numbers. These low Mach numbers occur during the calculation of fluxes in transverse direction of the shock propagation, where the local velocity component vanishes. A centralized formulation of the HLLC flux is provided for this purpose, which allows for a simple reduction of nonlinear signal speeds. In contrast to other shock-stable versions of the HLLC flux, the resulting HLLC-LM flux reduces the inherent numerical dissipation of the scheme. The robustness of the proposed scheme is tested for a comprehensive range of cases involving strong shock waves. Three-dimensional single- and multi-component simulations are performed with high-order methods to demonstrate that the HLLC-LM flux also copes with latest challenges of compressible high-speed computational fluid dynamics. (C) 2020 The Author(s). Published by Elsevier Inc.

The grid-aligned shock instability prevents an accurate computation of high Mach number flows using low-dissipation shock-capturing methods. In particular one manifestation, the so-called carbuncle phenomenon, has been investigated by various different groups over the past decades. Nevertheless, the mechanism of this instability is still not fully understood and commonly is suppressed by the introduction of additional numerical dissipation. However, present approaches may either significantly deteriorate the resolution of complex flow evolutions or involve additional procedures to limit stabilization measures to the shock region. Instead of increasing the numerical dissipation, in this paper, we present an alternative approach that relates the problem to the low Mach number in transverse direction of the shock front. We show that the inadequate scaling of the acoustic dissipation in the low Mach number limit is the prime reason for the instability. Our approach is to increase the "numerical" Mach number locally whenever the advection dissipation is small compared to the acoustic dissipation. A very simple modification of the eigenvalue calculation in the Roe approximation leads to a scheme with less numerical dissipation than the original Roe flux which prevents the grid-aligned shock instability. The simplicity of the modification allows for a detailed investigation of multidimensional effects. By showing that modifications in flow direction affect the shock stability in the transverse directions we confirm the multidimensional nature of the instability. The efficiency and robustness of the modified scheme is demonstrated for a wide range of test cases that are known to be particularly prone to the shock instability. Moreover, the modified flux also is successfully applied to multi-phase flows. (C) 2019 Elsevier Inc. All rights reserved.

Modern applications of computational fluid dynamics involve complex interactions across scales such as shock interactions with turbulent structures and multiphase interfaces. Such phenomena, which occur at very small physical viscosity, require high-resolution and low-dissipation compressible flow solvers. Many recent publications have focused on the design of high-order accurate numerical schemes and provide e.g. weighted essentially non-oscillatory (WENO) stencils up to 17th order for this purpose. As shown in detail by different authors, such schemes tremendously decrease adverse effects of numerical dissipation. However, such schemes are prone to numerically induced symmetry breaking which renders validation for the targeted problem range problematic. In this paper, we show that symmetry-breaking relates to vanishing numerical viscosity and is driven systematically by algorithmic floating-point effects which are no longer hidden by numerical dissipation. We propose a systematic procedure to deal with such errors by numerical and algorithmic formulations which respect floating-point arithmetic. We show that by these procedures inherent symmetries are preserved for a broad range of test cases with high-order shock-capturing schemes in particular in the high-resolution limit for both 2D and 3D. (C) 2019 The Authors. Published by Elsevier Ltd.