Bin Xie

A multi-moment finite volume method for incompressible Navier-Stokes equations on unstructured grids

A robust and accurate finite volume method (FVM) is proposed for incompressible viscous fluid dynamics on triangular and tetrahedral unstructured grids. Differently from conventional FVM where the volume integrated average (VIA) value is the only computational variable, the present formulation treats both VIA and the point value (PV) as the computational variables which are updated separately at each time step. The VIA is computed from a finite volume scheme of flux form, and is thus numerically conservative. The PV is updated from the differential form of the governing equation that does not have to be conservative but can be solved in a very efficient way. Including PV as the additional variable enables us to make higher-order reconstructions over compact mesh stencil to improve the accuracy, and moreover, the resulting numerical model is more robust for unstructured grids.We present the numerical formulations in both two and three dimensions on triangular and tetrahedral mesh elements. Numerical results of several benchmark tests are also presented to verify the proposed numerical method as an accurate and robust solver for incompressible flows on unstructured grids.

Short note: An interface capturing method with a continuous function: The THINC method on unstructured triangular and tetrahedral meshes

A novel interface-capturing method is proposed to compute moving interfaces on unstructured grids with triangular (2D) and tetrahedral (3D) elements. Different from the conventional VOF (volume of fluid) method which involves geometric reconstructions of the interface, the present method is based on the algebraic reconstruction approach originally developed in the THINC (tangent of hyperbola interface capturing) scheme by Xiao et al. (2005) [17]. A continuous multidimensional hyperbolic tangent function is employed for retrieving the jump-like distribution of the indicator function, which avoids the explicit geometric representation of the interface and thus substantially reduces the algorithmic complexity in unstructured grids. Numerical diffusion and smearing are effectively eliminated, and the compact thickness of the jump transition layer in the volume fraction is retained throughout the computation even for largely deformed interface. The solution quality of the present scheme is comparable to the VOF method with PLIC (piecewise linear interface calculation) algorithm.

A multi-moment constrained finite volume method on arbitrary unstructured grids for incompressible flows

We proposed a multi-moment constrained finite volume method which can simulate incompressible flows of high Reynolds number in complex geometries. Following the underlying idea of the volume-average/point-value multi-moment (VPM) method (Xie et al. (2014) [71]), this formulation is developed on arbitrary unstructured hybrid grids by employing the point values (PV) at both cell vertex and barycenter as the prognostic variables. The cell center value is updated via an evolution equation derived from a constraint condition of finite volume form, which ensures the rigorous numerical conservativeness. Novel numerical formulations based on the local PVs over compact stencil are proposed to enhance the accuracy, robustness and efficiency of computations on unstructured meshes of hybrid and arbitrary elements. Numerical experiments demonstrate that the present numerical model has nearly 3-order convergence rate with numerical errors much smaller than the VPM method. The numerical dissipation has been significantly suppressed, which facilitates numerical simulations of high Reynolds number flows in complex geometries.

A hybrid pressuredensity-based Mach uniform algorithm for 2D Euler equations on unstructured grids by using multi-moment finite volume method

We propose a novel Mach-uniform numerical model for 2D Euler equations on unstructured grids by using multi-moment finite volume method. The model integrates two key components newly developed to solve compressible flows on unstructured grids with improved accuracy and robustness. A new variant of AUSM scheme, so-called AUSM+-pcp (AUSM+ with pressure-correction projection), has been devised including a pressure-correction projection to the AUSM+ flux splitting, which maintains the exact numerical conservativeness and works well for all Mach numbers. A novel 3th-order, non-oscillatory and less-dissipative reconstruction has been proposed by introducing a multi-dimensional limiting and a BVD (boundary variation diminishing) treatment to the VPM (volume integrated average (VIA) and point value (PV) based multi-moment) reconstruction. The resulting reconstruction scheme, the limited VPM-BVD formulation, is able to resolve both smooth and non-smooth solutions with high fidelity. Benchmark tests have been used to verify the present model. The numerical results substantiate the present model as an accurate and robust unstructured-grid formulation for flows of all Mach numbers.

Simulation and mitigation of the magneto-Rayleigh-Taylor instabilities in Z-pinch gas discharge extreme ultraviolet plasma radiation sources

The development and use of a single-fluid two-temperature approximated 2-D Magneto-Hydrodynamics code is reported. Z-pinch dynamics and the evolution of Magneto-Rayleigh-Taylor (MRT) instabilities in a gas jet type Extreme Ultraviolet (EUV) source are investigated with this code. The implosion and stagnation processes of the Z-pinch dynamics and the influence of initial perturbations (single mode, multi- mode, and random seeds) on MRT instability are discussed in detail. In the case of single mode seeds, the simulation shows that the growth rates for mm-scale wavelengths up to 4u2009mm are between 0.05 and 0.065 ns−1. For multi-mode seeds, the mode coupling effect leads to a series of other harmonics, and complicates MRT instability evolution. For perturbation by random seeds, the modes evolve to longer wavelengths and finally converge to a mm-scale wavelength approximately 1u2009mm. MRT instabilities can also alter the pinch stagnation state and lead to temperature and density fluctuations along the Z axis, whic...

Accurate and robust PISO algorithm on hybrid unstructured grids using the multimoment finite volume method

ABSTRACT This paper presents a novel numerical model for incompressible flows on unstructured hybrid grids by combining the pressure-implicit with splitting of operator (PISO) algorithm and volume-integrated average and point value-based multimoment (VPM) method. Implementing the spatial discretization of VPM to the PISO solution procedure results in a novel formulation that is unconditionally stable and superior in numerical accuracy and robustness in comparison with the conventional finite volume method. The present VPM/PISO formulation provides a numerical framework of great practical significance that well balances the numerical accuracy and algorithmic complexity. Numerical verifications demonstrate that the present model can significantly improve numerical accuracy. Moreover, the numerical dissipation is effectively suppressed, which shows a great potential for simulations of high-Reynolds number flows.

High fidelity discontinuity-resolving reconstruction for compressible multiphase flows with moving interfaces

Abstract We present in this work a new reconstruction scheme, so-called MUSCL-THINC-BVD scheme, to solve the five-equation model for interfacial two phase flows. This scheme employs the traditional shock capturing MUSCL (Monotone Upstream-centered Schemes for Conservation Law) scheme as well as the interface sharpening THINC (Tangent of Hyperbola for INterface Capturing) scheme as two building-blocks of spatial reconstruction on the BVD (boundary variation diminishing) principle that minimizes the variations (jumps) of the reconstructed variables at cell boundaries, and thus effectively reduces the dissipation error in numerical solutions. The MUSCL-THINC-BVD scheme is implemented to the volume fraction and other state variables under the same finite volume framework, which realizes the consistency among volume fraction and other physical variables. Numerical results of benchmark tests show that the present method is able to capture the material interface as a well-defined sharp jump in volume fraction, and obtain numerical solutions of superior quality in comparison to other existing methods. The proposed scheme is a simple and effective method of practical significance for simulating compressible interfacial multiphase flows.

A non-oscillatory multi-moment finite volume scheme with boundary gradient switching

In this work we propose a new formulation for high-order multi-moment constrained finite volume (MCV) method. In the one-dimensional building-block scheme, three local degrees of freedom (DOFs) are equidistantly defined within a grid cell. Two candidate polynomials for spatial reconstruction of third-order are built by adopting one additional constraint condition from the adjacent cells, i.e. the DOF at middle point of left or right neighbour. A boundary gradient switching (BGS) algorithm based on the variation-minimization principle is devised to determine the spatial reconstruction from the two candidates, so as to remove the spurious oscillations around the discontinuities. The resulted non-oscillatory MCV3-BGS scheme is of fourth-order accuracy and completely free of case-dependent ad hoc parameters. The widely used benchmark tests of one- and two-dimensional scalar and Euler hyperbolic conservation laws are solved to verify the performance of the proposed scheme in this paper. The MCV3-BGS scheme is very promising for the practical applications due to its accuracy, non-oscillatory feature and algorithmic simplicity.

A Robust and Practical Multi-Moment Finite Volume Model for Computational Fluid Dynamics

A robust and practical CFD code has been developed. The numerical framework, so-called VSIAM3 (Volume/Surface Integrated Average based Multi-Moment Method) makes use of two kinds of integrated moments of physical field, i.e. the volume integrated average (VIA) and the surface integrated average (SIA), which are treated as the computational variables and separately updated in time. VSIAM3 formulation is essentially different from conventional finite volume method and provides a convenient and robust framework to accommodate many existing numerical techniques for simulating various complex flows. In this paper, we will present the underlying idea of VSIAM3 and the extensions to make it applicable to various practical problems. Efforts toward high computational performance on hard wares with distributed memory and GPGPU will be also reported.

A 3D Numerical Model for Free Interfacial Flows and Applications to Offshore Waves with Submerged Obstacles

A 3D numerical model for incompressible multi-fluid flows has been developed by using a multi-moment finite volume method and an accurate and efficient VOF type scheme for capturing moving interfaces of multi-fluids. The numerical model is validated with the theoretical and experimental results of the benchmark tests of solitary wave and dam break flow, which indicates the adequate numerical accuracy of the model as a practical tool to assess and predict offshore waves and their impacts on coastal structures. Numerical experiments have been systematically conducted to investigate wave breaking phenomena and the impacts on seawalls.