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In this paper, we present exact Riemann solvers for the Riemann problem and the half Riemann problem, respectively, for one‐dimensional multi‐material elastic‐plastic flows with the Mie‐Grüneisen equation of state(EOS), hypo‐elastic constitutive model and the von Mises' yielding condition. We firstly analyze the Jacobian matrices in the elastic and plastic states, and then build the relations of different variables across different type of waves. Based on these formulations, an exact Riemann solver is constructed with totally thirty‐six possible cases of wave structures. A large number of tests prove the rightness of the new exact Riemann solver. Moreover, an exact Riemann solver is also deduced for the half Riemann problem and its validity is tested by two examples.

► A robust overset assembly method for multiple overlapping bodies

15 Sep, 2020

1. We present a new overset assembly method allowing for multiple overlapping bodies by searching the donor cell before identifying the interpolation boundary. 2. It shows good ability to eliminate “isolated island” and “orphan point” problems by selecting interpolation cells only in areas with donor cells. 3. It was properly validated by several cases and the efficiency of the overset assembly was significantly higher than other similar overset assembly programs.

Summary

A robust overset assembly method allowing for multiple overlapping bodies is presented. This method extends the overset assembly method to deal with the interference between objects and prevents the failure of the search for donor cells due to the complex shape of the models. The donor cells are searched before identifying the boundary of the chimera interpolation. By selecting interpolation cells only in areas with donor cells, the final overset interpolation boundary cells can always find their donor cells, which prevents orphan points and achieves excellent robustness. First, the implementation of the proposed assembly method is described in detail. Subsequently, the usability and efficiency of the method are verified using several cases. Finally, the integration strategy of the computational fluid dynamics solver based on overset interpolation with the modification of the boundary type is described and verified using practical cases with overlapping bodies. The results demonstrate the applicability of the proposed overset grid assembly method.

► Basic verification of a numerical framework applied to a morphology adaptive multifield two‐fluid model considering bubble motions

15 Sep, 2020

A multifield two‐fluid model is proposed, allowing for adaptive switching between different flow morphologies. A compact momentum interpolation method for multiphase flows is applied and virtual mass consistently added to this approach. Large‐scale interfaces are described with an appropriate drag model formulation and the stiff system is approximately resolved with a partial‐elimination algorithm, which is extended to multiple phases via a sum formulation. Solver capabilities are demonstrated in cases, where disperse and multiple continuous phases occur in the same location.

Summary

A morphology adaptive modeling framework is derived that is able to handle computationally efficiently dispersed as well as resolved interfacial structures coexisting in the computational domain with the same set of equations. The Eulerian multifield two‐fluid model is combined with the compact momentum interpolation method for multiple phases, which has been proposed in the literature as an extension to the Rhie‐Chow pressure‐velocity coupling. Additionally to the interfacial drag force, the virtual mass force is consistently accounted for in the model. Utilizing a specialized interfacial drag formulation, large interfacial structures can be described with the presented method in a volume‐of‐fluid‐like manner, additionally to the disperse description. The strong phase coupling due to the drag closure model in interfacial regions is resolved with a partial elimination algorithm, which is adapted to work in an approximate manner for more than two phases via a sum formulation. The presented model is implemented in the C++ library OpenFOAM and solver performance is compared with results obtained with the homogeneous model approach in two cases of a single rising gas bubble for two‐ and three‐dimensional space, respectively. Additionally, for both three‐dimensional cases, the results are compared with experimental data. Finally, the presented method's capability of representing dispersed and resolved interfacial structures at the same time is demonstrated with two test cases: a two‐dimensional gas bubble, rising in a liquid, which is laden with micro gas bubbles, and a two‐dimensional stagnant stratification of water and oil, sharing a large‐scale interface, which is penetrated by micro gas bubbles.

► Large‐scale simulation of shallow water waves via computation only on small staggered patches

13 Sep, 2020

Abstract

Amultiscale computational scheme is developed to use given small micro‐scale simulations of complicated physicalwave processes to empower macro‐scale system‐level predictions. By coupling small patches of simulations over unsimulated space, large savings in computational time are realisable. Here we generalise the patch scheme to the case of wave systems on staggered grids in 2D space. Classic macro‐scale interpolation provides a generic coupling between patches that achieves consistency between the emergent macro‐scale simulation and the underlying micro‐scale dynamics. Spectral analysis indicates that the resultant scheme empowers feasible computation of large macro‐scale simulations of wave systems even with complicated underlying physics. As a example of the scheme’s application, we use it to simulate some simple scenarios of a given turbulent shallow water model.

► A stable hybrid Roe scheme on triangular grids

13 Sep, 2020

Summary

Numerical shock instability is a common problem for shock‐capturing methods that try to resolve contact and shear waves with minimal diffusion. Most flux‐difference splitting and the AUSM family of schemes produce the carbuncle phenomenon on both structured and unstructured grids. The original Roe scheme is well known to generate shock anomalies and can lead to non‐entropic weak solutions to the Euler equations. A simple and robust approach for healing these numerical instabilities is to apply the hybrid technique incorporated with an efficient weighting switch function to control the amount of dissipation in the vicinity of shock waves. This paper proposes a simple, robust, and accurate hybrid Roe scheme (Roe⁺ scheme) by hybridizing the Roe scheme and the modified AUSMV⁺ scheme. A new normalized pressure/density‐based weighting switch function is proposed and applied to the scheme to minimize the numerical dissipation and maintain the robustness of the hybridization. The linearized discrete analysis is performed to evaluate the proposed scheme according to the perturbation damping mechanism of an odd‐even decoupling problem. The resulting recursive equations indicate that the hybridized mechanism damps all perturbations effectively. Finally, several numerical examples demonstrated that the Roe+ scheme provides an accurate, robust, and carbuncle‐free solution on both structured and unstructured triangular grids.

► A multipoint flux approximation with diamond stencil finite volume scheme for the two‐dimensional simulation of fluid flows in naturally fractured reservoirs using a hybrid‐grid method

11 Sep, 2020

$A multipoint flux approximation with diamond stencil finite volume scheme for the two‐dimensional simulation of fluid flows in naturally fractured reservoirs using a hybrid‐grid method$

This paper demonstrates the capability of the MPFA‐D, coupled with a hybrid‐grid scheme, to model two‐phase flows in a naturally fractured porous media, with channels or barriers in different spatial positions, using unstructured grids, under any permeability tensors.

Summary

Two‐phase flows of oil and water in naturally fractured reservoirs can be described by a system of nonlinear partial differential equations that comprises of an elliptic pressure equation and hyperbolic saturation equation coupled through the total velocity field. Modeling this problem is a great challenge, due to the complexity of the depositional environments, including inclined layers and fractures with different sizes and shapes, and random spatial distribution. In this work, to solve the pressure equation, we adopted a cell‐centered finite‐volume method with a multipoint flux approximation that uses the “diamond stencil” (MPFA‐D) coupled with a hybrid‐grid method (HyG) to deal with the fractures. The classical first‐order upwind method was used to solve the saturation equation, in its explicit and implicit versions. The MPFA‐D is a very robust and flexible formulation that is capable of handling highly heterogeneous and anisotropic domains using general polygonal meshes. In the strategy developed in this work, the mesh that discretize the domain must fit the spatial position of the fractures, so that they are associated to the control surfaces—as (n − 1)D cells—therefore, the calculation of the fluxes in these control surfaces is dependent on the pressures on fractures and on the adjacent volumes. In HyG, the fractures are expanded to nD in the computational domain. The proposed formulation presented quite remarkable results when compared with similar formulations using classical full pressure support and triangle pressure support methods, or even the with MPFA‐D itself when the fractures are treated as nD geometric entities.

► The double‐tree method: An O(n) unsteady aerodynamic lifting surface method

11 Sep, 2020

A new method for reducing the computational cost of the unsteady vortex lattice method is introduced. The method reduces the order of computations from O(n ²) to O(n) by utilizing two tree structures in tandem. A number of case studies are analyzed to verify its effectiveness and show how the accuracy/efficiency trade‐off can be controlled.

Summary

Two new methods for reducing the computational cost of the unsteady vortex lattice method are developed. These methods use agglomeration to construct time‐saving tree structures by approximating the effect of either a group of vortex rings or query points. A case study shows that combining the two new O(n·log n) tree methods together results in an O(n) method, called the double‐tree method. Other case studies show that the trade‐off between accuracy and speed can be easily and reliably controlled by the agglomeration cutoff distance. For a flat plate with 5 × 200 panels analyzed over 20 time steps, the double‐tree method is 7 times faster than the unsteady vortex lattice method with a <5% difference in the force distribution and total lift coefficient. The case studies suggest that the computational benefit will increase for the same level of accuracy if the size of the problem is increased, making the method beneficial for full‐aircraft analysis within optimization or dynamic load analysis, where the computational cost of the unsteady vortex lattice method can be large.

► A third‐order compact nonlinear scheme for compressible flow simulations

11 Sep, 2020

Simulation of Rayleigh‐Taylor instability problem: The proposed scheme, TCNS, together with an accurate/less dissipative Riemann solver, HLLC, obtains significantly high resolutions for small scales

Summary

Reynolds‐averaged Navier‐Stokes simulations based on second‐order numerical methods are widely used by commercial codes and work as dominating tools for most industrial applications. They, however, suffer from limitations in accurate and reliable predictions of skin‐friction drag and aerodynamic heating, as well as in simulations of complex flows such as large‐scale separation and transition. A remedy for this is the development of high‐order schemes, by which numerically induced dissipation and dispersion errors of low‐order schemes can be effectively reduced. Weighted compact nonlinear schemes (WCNSs) are a family of high‐resolution nonlinear shock‐capturing methods. A stencil‐selection procedure is introduced in the proposed work with an aim to improve the nonlinear weight of the third‐order WCNS. By using the approximate dispersion relation analysis, it is demonstrated that the new scheme has reduced dissipation and dispersion errors, compared with WCNSs using two typical nonlinear weights. Improvements are also achieved by the new scheme in numerical tests such as the double Mach reflection problem and the Rayleigh‐Taylor instability simulation, which are characterized by strong shock discontinuities and rich small scales, respectively. The new scheme is therefore highly favored in the simulation of flow problems involving strong discontinuities and multiscales phenomena.

► Simulation of compressibility of entrapped air in an incompressible free surface flow using a pressure‐based method for unified equations

11 Sep, 2020

In this article, a pressure‐based method is developed to solve the unified conservation laws for incompressible and compressible fluids. The proposed method is validated based on the comparison of the pressure fluctuations due to an oscillating water column in a closed tube and a free drop of a liquid block in a tank. The developed code is applied to simulate the compression and expansion of the entrapped air in a dam break flow.

Summary

A pressure‐based method is developed to solve the unified conservation laws for incompressible and compressible fluids. A polytropic law is used to model the compressibility of a gas and decouple the energy equation. The pressure field is calculated by solving a single‐pressure Poisson equation for the entire flow domain. The effects of the compressibility of the gas are reflected in the source term of the Poisson equation. The continuities of pressure and normal velocity across a material interface are achieved without any additional treatment along the interface. To validate the developed method, the oscillation of a water column in a closed tube due to the compression and expansion of air in the tube is simulated. The computed time history of the pressure at the end wall of the tube is in good agreement with other computational results. The free drop of a water column in a closed tank is simulated. The time history of the pressure at the center of the bottom of the tank shows good agreement with other reported results. The developed code is applied to simulate the air cushion effect of entrapped air in a dam break flow. The computed result is in good agreement with other experimental and computational results until the air is entrapped. As the entrapped air pocket undergoes rapid pulsation, the pressure field of water around the air pocket oscillates synchronously.

► A proper orthogonal decomposition variational multiscale meshless interpolating element‐free Galerkin method for incompressible magnetohydrodynamics flow

11 Sep, 2020

Summary

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element‐free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced‐order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced‐order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two‐dimensional cases.