An improved numerical solver for the unified solution of compressible and incompressible fluids involving interfaces is proposed. The present method is based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified Procedure) method, which is a pressure-based semi-implicit solver for the Euler equations of fluid flows. In Part I of this series of articles [M. Ida, Comput. Phys. Commun. 132 (2000) 44], we proposed an improved scheme for the convection terms in the equations, which allowed us discontinuous descriptions of the density interface by replacing the cubic interpolation function used in the CIP scheme with a quadratic extrapolation function only around the interface. In this paper, as Part II of this series, the multi-time-step integration technique is adapted to the CIP-CUP integration. Because the CIP-CUP treats different-nature components in the fluid equations separately, the adaptation of the technique is straightforward. This modification allows us flexible determinations of the time interval, which results in an efficient and accurate integration. Furthermore, some additional discussion on our methods is presented. Finally, the application results to composite flow problems such as compressible and incompressible Kelvin-Helmholtz instabilities and the dynamics of two acoustically coupled deformable bubbles in a viscous liquid are provided.
Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, $\mathrm{M}\approx 0.1$, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to a genuinely incompressible formulation. Our…
The majority of available numerical algorithms for interfacial two-phase flows either treat both fluid phases as incompressible (constant density) or treat both phases as compressible (variable density). This presents a limitation for the prediction of many two-phase flows, such as subsonic fuel injection, as treating both phases as compressible is computationally expensive due to the very stiff pressure-density-temperature coupling of liquids. A framework with the capability of treating one phase compressible and the other phase incompressible, therefore, has a significant potential to improv…
Gas bubbles immersed in a liquid and flowing through a large pressure gradient undergoes volumetric deformation in addition to possible deviatoric deformation. While the high density liquid phase can be assumed to be an incompressible fluid, the gas phase needs to be modelled as a compressible fluid for such bubble flow problems. The Rayleigh--Plesset (RP) equation describes such a bubble undergoing volumetric deformation due to changes in pressure in the ambient incompressible fluid, assuming axisymmetric dynamics. We propose a compressible-incompressible coupling of Smoothed Particle Hydrody…
Pinned surface and frozen surface approximations are two commonly used approximations for the boundary conditions at the exposed surfaces of semiconductor structures. We have studied the effect of pinned surface and frozen surface boundary conditions on the spatial distribution of compressible and incompressible strips observed in the two dimensional electron gas formed in a GaAs/AlGaAs heterostructure under quantum Hall effect regime. We have used semi classical Thomas-Fermi method for describing the many body problem along with the Poisson equation for electrostatics. We observe that the bou…
We discuss hybrid atomistic-continuum methods for multiscale hydrodynamic applications. Both dense fluid and dilute gas formulations are considered. The choice of coupling method and its relation to the fluid physics is discussed. The differences in hybrid methods resulting from underlying compressible and incompressible continuum formulations as well as the importance of timescale decoupling are highlighted. We also discuss recently developed compressible and incompressible hybrid methods for dilute gases. The incompressible framework is based on the Schwarz alternating method whereas the com…
At high Reynolds numbers, the use of explicit in time compressible flow simulations with spectral/$hp$ element discretization can become significantly limited by time step. To alleviate this limitation we extend the capability of the spectral/$hp$ element open-source software framework, Nektar++, to include an implicit discontinuous Galerkin compressible flow solver. The integration in time is carried out by a singly diagonally implicit Runge-Kutta method. The non-linear system arising from the implicit time integration is iteratively solved by the Jacobian-free Newton Krylov (JFNK) method. A …
The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and hydraulic waves existing at vastly different spatial and temporal scales. If simulated on the same numerical grid, the need for accuracy in hydraulic waves will necessitate an exaggerated resolution of acoustic waves. Likewise, time steps restricted by the speed of sound are small compared to the time scales active in hydraulic waves. This constitutes a waste of…
A modified HLLC-type contact preserving Riemann solver for incompressible two-phase flows using the artificial compressibility formulation is presented. Here, the density is omitted from the pressure evolution equation. Also, while calculating the eigenvalues and eigenvectors, the variations of the volume fraction is taken into account. Hence, the equations for the intermediate states and the intermediate wave speed are different from the previous HLLC-VOF formulation [Bhat S P and Mandal J C, J. Comput. Phys. 379 (2019), pp. 173-191]. Additionally, an interface compression algorithm is used i…
The HLLC Riemann solver, which resolves both the shock waves and contact discontinuities, is popular to the computational fluid dynamics community studying compressible flow problems with mesh methods. Although it was reported to be used in meshless methods, the crucial information and procedure to realise this scheme within the framework of meshless methods were not clarified fully. Moreover, the capability of the meshless HLLC solver to deal with compressible liquid flows is not completely clear yet as very few related studies have been reported. Therefore, a comprehensive investigation of a…
We present STREAmS, an in-house high-fidelity solver for large-scale, massively parallel direct numerical simulations (DNS) of compressible turbulent flows on graphical processing units (GPUs). STREAmS is written in the Fortran 90 language and it is tailored to carry out DNS of canonical compressible wall-bounded flows, namely turbulent plane channel, zero-pressure gradient turbulent boundary layer and supersonic oblique shock-wave/boundary layer interactions. The solver incorporates state-of-the-art numerical algorithms, specifically designed to cope with the challenging problems associated w…
The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics) platform. The resulting solver is fully implicit and able to simulate compressible flow problems governed by either the Euler or the Navier-Stokes equations in two and three dimensions. Furthermore, it can run in parallel on multiple CPU-cores and is designed to handle unstructured grids consisting of both straight and curved edged quadrilateral or hexahedral elem…
A conservative finite-volume framework, based on a collocated variable arrangement, for the simulation of flows at all speeds, applicable to incompressible, ideal-gas and real-gas fluids is proposed in conjunction with a fully-coupled pressure-based algorithm. The applied conservative discretisation and implementation of the governing conservation laws as well as the definition of the fluxes using a momentum-weighted interpolation are identical for incompressible and compressible fluids, and are suitable for complex geometries represented by unstructured meshes. Incompressible fluids are descr…
The Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) method is a Lagrangian method that is typically used for the simulation of incompressible fluids. While developing an SPH-based scheme or solver, researchers often verify their code with exact solutions, solutions from other numerical techniques, or experimental data. This typically requires a significant amount of computational effort and does not test the full capabilities of the solver. Furthermore, often this does not yield insights on the convergence of the solver. In this paper we introduce the method of manufactured solutio…
Non-ideal state equations are needed to compute a growing number of engineering-relevant problems. The additional computational overhead from the complex thermodynamics accounts for a significant portion of the total computation, especially the near-critical or transcritical thermodynamic regimes. A compromise between computational speed and the accuracy of the thermodynamic property evaluations results in a propagation of the error from the thermodynamics to the hydrodynamic computations. This work proposes a systematic error quantification and computational cost estimate of the various appro…
The purpose of this paper is to extend the versatile mixed methods originally developed by Chen and Williams for isothermal flows in "Versatile Mixed Methods for the Incompressible Navier-Stokes Equations," Computers & Mathematics with Applications, 2020, (under review), to simulate non-isothermal incompressible flows. These new mixed methods are particularly interesting, as with only minor modifications they can be applied to a much broader range of flows, including non-isothermal weakly-compressible flows, and fully-compressible flows. In the main body of this paper, we carefully develop the…
This work presents a review of high-order hybridisable discontinuous Galerkin (HDG) methods in the context of compressible flows. Moreover, an original unified framework for the derivation of Riemann solvers in hybridised formulations is proposed. This framework includes, for the first time in an HDG context, the HLL and HLLEM Riemann solvers as well as the traditional Lax-Friedrichs and Roe solvers. HLL-type Riemann solvers demonstrate their superiority with respect to Roe in supersonic cases due to their positivity preserving properties. In addition, HLLEM specifically outstands in the appro…
We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically-rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and…
This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected convergence rates and remains stable for extremely small values of the characteristic Mach number. The staggered spatial discretization on the MAC stencil, commonly used in numerical methods for incompressible Navier-Stokes equations, was found to be convenient for the discretization of the compressible Navier-Stokes equations written in the non-conservative form…
