共查询到10条相似文献,搜索用时 0 毫秒
1.
Ruo Li & Wei Zhong 《Communications In Computational Physics》2021,30(5):1545-1588
We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. Theproposed schemes admit an extensive permitted range of the parameters in the mapping functions. Consequently, they have the capacity to achieve optimal convergencerates, even near critical points. Particularly, the new schemes with fine-tuned parameters illustrates a significant advantage when solving problems with discontinuities. Itproduces numerical solutions with high resolution without generating spurious oscillations, especially for long output times. 相似文献
2.
In this paper, a new five-point targeted essentially non-oscillatory (TENO)scheme with adaptive dissipation is proposed. With the standard TENO weightingstrategy, the cut-off parameter $C_T$ determines the nonlinear numerical dissipation ofthe resultant TENO scheme. Moreover, according to the dissipation-adaptive TENO5-A scheme, the choice of the cut-off parameter $C_T$ highly depends on the effective scalesensor. However, the scale sensor in TENO5-A can only roughly detect the discontinuity locations instead of evaluating the local flow wavenumber as desired. In thiswork, a new five-point scale sensor, which can estimate the local flow wavenumber accurately, is proposed to further improve the performance of TENO5-A. In combinationwith a hyperbolic tangent function, the new scale sensor is deployed to the TENO5-Aframework for adapting the cut-off parameter $C_T,$ i.e., the local nonlinear dissipation,according to the local flow wavenumber. Overall, sufficient numerical dissipation isgenerated to capture discontinuities, whereas a minimum amount of dissipation is delivered for better resolving the smooth flows. A set of benchmark cases is simulated todemonstrate the performance of the new TENO5-A scheme. 相似文献
3.
In this paper, a high-order moment-based multi-resolution Hermiteweighted essentially non-oscillatory (HWENO) scheme is designed for hyperbolic conservation laws. The main idea of this scheme is derived from our previous work [J.Comput. Phys., 446 (2021) 110653], in which the integral averages of the function andits first order derivative are used to reconstruct both the function and its first orderderivative values at the boundaries. However, in this paper, only the function values atthe Gauss-Lobatto points in the one or two dimensional case need to be reconstructedby using the information of the zeroth and first order moments. In addition, an extramodification procedure is used to modify those first order moments in the troubled-cells, which leads to an improvement of stability and an enhancement of resolutionnear discontinuities. To obtain the same order of accuracy, the size of the stencil required by this moment-based multi-resolution HWENO scheme is still the same as thegeneral HWENO scheme and is more compact than the general WENO scheme. Moreover, the linear weights are not unique and are independent of the node position, andthe CFL number can still be 0.6 whether for the one or two dimensional case, which hasto be 0.2 in the two dimensional case for other HWENO schemes. Extensive numericalexamples are given to demonstrate the stability and resolution of such moment-basedmulti-resolution HWENO scheme. 相似文献
4.
Yifei Wan & Yinhua Xia 《Communications In Computational Physics》2023,33(5):1270-1331
For steady Euler equations in complex boundary domains, high-order shockcapturing schemes usually suffer not only from the difficulty of steady-state convergence but also from the problem of dealing with physical boundaries on Cartesian
grids to achieve uniform high-order accuracy. In this paper, we utilize a fifth-order
finite difference hybrid WENO scheme to simulate steady Euler equations, and the
same fifth-order WENO extrapolation methods are developed to handle the curved
boundary. The values of the ghost points outside the physical boundary can be obtained by applying WENO extrapolation near the boundary, involving normal derivatives acquired by the simplified inverse Lax-Wendroff procedure. Both equivalent expressions involving curvature and numerical differentiation are utilized to transform
the tangential derivatives along the curved solid wall boundary. This hybrid WENO
scheme is robust for steady-state convergence and maintains high-order accuracy in
the smooth region even with the solid wall boundary condition. Besides, the essentially non-oscillation property is achieved. The numerical spectral analysis also shows
that this hybrid WENO scheme has low dispersion and dissipation errors. Numerical
examples are presented to validate the high-order accuracy and robust performance of
the hybrid scheme for steady Euler equations in curved domains with Cartesian grids. 相似文献
5.
Jun Zhu & Jianxian Qiu 《Communications In Computational Physics》2020,27(3):897-920
In this paper, a new type of third-order and fourth-order weighted essentially non-oscillatory (WENO) schemes is designed for simulating the Hamilton-Jacobi equations on triangular meshes. We design such schemes with the use of the nodal information defined on five unequal-sized spatial stencils, the application of monotone Hamiltonians as a building block, the artificial set of positive linear weights to make up high-order approximations in smooth regions simultaneously avoiding spurious oscillations nearby discontinuities of the derivatives of the solutions. The spatial reconstructions are convex combinations of the derivatives of a modified cubic/quartic polynomial defined on a big spatial stencil and four quadratic polynomials defined on small spatial stencils, and a third-order TVD Runge-Kutta method is used for the time discretization. The main advantages of these WENO schemes are their efficiency, simplicity, and can be easily implemented to higher dimensional unstructured meshes. Extensive numerical tests are performed to illustrate the good performance of such new WENO schemes. 相似文献
6.
Zheng Sun Shuyi Wang Lo-Bin Chang Yulong Xing & Dongbin Xiu 《Communications In Computational Physics》2020,28(5):2075-2108
We propose a universal discontinuity detector using convolution neural network (CNN) and apply it in conjunction of solving nonlinear conservation laws in both1D and 2D. The CNN detector is trained offline with synthetic data. The training dataare generated using randomly constructed piecewise functions, which are then processed using randomized linear advection solver to count for the cases of numericalerrors in practice. The detector is then paired with high-order numerical solvers. Inparticular, we combined high-order WENO in troubled cells with high-order centraldifference in smooth region. Extensive numerical examples are presented. We observethat the proposed method produces notably sharper and cleaner signals near the discontinuities, when compared to other well known troubled cell detector methods. 相似文献
7.
High-Order Local Discontinuous Galerkin Method with Multi-Resolution WENO Limiter for Navier-Stokes Equations on Triangular Meshes 下载免费PDF全文
Yizhou Lu Jun Zhu Shengzhu Cui Zhenming Wang Linlin Tian & Ning Zhao 《Communications In Computational Physics》2023,33(5):1217-1239
In this paper, a new multi-resolution weighted essentially non-oscillatory(MR-WENO) limiter for high-order local discontinuous Galerkin (LDG) method is designed for solving Navier-Stokes equations on triangular meshes. This MR-WENOlimiter is a new extension of the finite volume MR-WENO schemes. Such new limiteruses information of the LDG solution essentially only within the troubled cell itself, tobuild a sequence of hierarchical $L^2$ projection polynomials from zeroth degree to thehighest degree of the LDG method. As an example, a third-order LDG method with associated same order MR-WENO limiter has been developed in this paper, which couldmaintain the original order of accuracy in smooth regions and could simultaneouslysuppress spurious oscillations near strong shocks or contact discontinuities. The linear weights of such new MR-WENO limiter can be any positive numbers on conditionthat their summation is one. This is the first time that a series of different degree polynomials within the troubled cell are applied in a WENO-type fashion to modify thefreedom of degrees of the LDG solutions in the troubled cell. This MR-WENO limiteris very simple to construct, and can be easily implemented to arbitrary high-order accuracy and in higher dimensions on unstructured meshes. Such spatial reconstructionmethodology improves the robustness in the numerical simulation on the same compact spatial stencil of the original LDG methods on triangular meshes. Some classicalviscous examples are given to show the good performance of this third-order LDGmethod with associated MR-WENO limiter. 相似文献
8.
Continuous Finite Element Subgrid Basis Functions for Discontinuous Galerkin Schemes on Unstructured Polygonal Voronoi Meshes 下载免费PDF全文
Walter Boscheri Michael Dumbser & Elena Gaburro 《Communications In Computational Physics》2022,32(1):259-298
We propose a new high order accurate nodal discontinuous Galerkin (DG)method for the solution of nonlinear hyperbolic systems of partial differential equations (PDE) on unstructured polygonal Voronoi meshes. Rather than using classicalpolynomials of degree $N$ inside each element, in our new approach the discrete solutionis represented by piecewise continuous polynomials of degree $N$ within each Voronoi element, using a continuous finite element basis defined on a subgrid inside each polygon.We call the resulting subgrid basis an agglomerated finite element (AFE) basis for the DGmethod on general polygons, since it is obtained by the agglomeration of the finite element basis functions associated with the subgrid triangles. The basis functions on eachsub-triangle are defined, as usual, on a universal reference element, hence allowing tocompute universal mass, flux and stiffness matrices for the subgrid triangles once andfor all in a pre-processing stage for the reference element only. Consequently, the construction of an efficient quadrature-free algorithm is possible, despite the unstructurednature of the computational grid. High order of accuracy in time is achieved thanksto the ADER approach, making use of an element-local space-time Galerkin finite element predictor.The novel schemes are carefully validated against a set of typical benchmark problems for the compressible Euler and Navier-Stokes equations. The numerical resultshave been checked with reference solutions available in literature and also systematically compared, in terms of computational efficiency and accuracy, with those obtainedby the corresponding modal DG version of the scheme. 相似文献
9.
Performance Enhancement for High-Order Gas-Kinetic Scheme Based on WENO-Adaptive-Order Reconstruction 下载免费PDF全文
Xing Ji & Kun Xu 《Communications In Computational Physics》2020,28(2):539-590
High-order gas-kinetic scheme (HGKS) has been well-developed in the past
years. Abundant numerical tests including hypersonic flow, turbulence, and aeroacoustic problems, have been used to validate its accuracy, efficiency, and robustness.
However, there is still room for its further improvement. Firstly, the reconstruction
in the previous scheme mainly achieves a fifth-order accuracy for the point-wise values at a cell interface due to the use of standard WENO reconstruction, and the slopes
of the initial non-equilibrium states have to be reconstructed from the cell interface
values and cell averages again. The same order of accuracy for slopes as the original
WENO scheme cannot be achieved. At the same time, the equilibrium state in space
and time in HGKS has to be reconstructed separately. Secondly, it is complicated to get
reconstructed data at Gaussian points from the WENO-type method in high dimensions. For HGKS, besides the point-wise values at the Gaussian points it also requires
the slopes in both normal and tangential directions of a cell interface. Thirdly, there exists visible spurious overshoot/undershoot at weak discontinuities from the previous
HGKS with the standard WENO reconstruction. In order to overcome these difficulties, in this paper we use an improved reconstruction for HGKS. The WENO with
adaptive order (WENO-AO) [2] method is implemented for reconstruction. Equipped
with WENO-AO reconstruction, the performance enhancement of HGKS is fully explored. WENO-AO not only provides the interface values, but also the slopes. In other
words, a whole polynomial inside each cell is provided by the WENO-AO reconstruction. The available polynomial may not benefit to the high-order schemes based on the
Riemann solver, where only points-wise values at the cell interface are needed. But,
it can be fully utilized in the HGKS. As a result, the HGKS becomes simpler than the
previous one with the direct implementation of cell interface values and their slopes
from WENO-AO. The additional reconstruction of equilibrium state at the beginning
of each time step can be avoided as well by dynamically merging the reconstructed non-equilibrium slopes. The new HGKS essentially releases or totally removes the
above existing problems in the previous HGKS. The accuracy of the scheme from 1D
to 3D from the new HGKS can recover the theoretical order of accuracy of the WENO
reconstruction. In the two- and three-dimensional simulations, the new HGKS shows
better robustness and efficiency than the previous scheme in all test cases. 相似文献
10.
Shuai Shao Ming Li Nianhua Wang & Laiping Zhang 《Communications In Computational Physics》2020,27(3):725-752
A new hybrid reconstruction scheme DDG/FV is developed in this work
by combining the DDG method and DG/FV hybrid scheme developed in the authors' previous work [1–4] to simulate three-dimensional compressible viscous flow on tetrahedral grids. The extended von Neumann stencils are used in the reconstruction process to ensure the linear stability, and the L2 projection and the least-squares method
are adopted to reconstruct higher order distributions for higher accuracy and robustness. In addition, a quadrature-free L2 projection based on orthogonal basis functions
is implemented to improve the efficiency of reconstruction. Three typical test cases,
including the 3D Couette flow, laminar flows over an analytical 3D body of revolution
and over a sphere, are simulated to validate the accuracy and efficiency of DDG/FV
method. The numerical results demonstrate that the DDG scheme can accelerate the
convergence history compared with widely-used BR2 scheme. More attractively, the
new DDG/FV hybrid method can deliver the same accuracy as BR2-DG method with
more than 2 times of efficiency improvement in solving 3D Navier-Stokes equations on
tetrahedral grids, and even one-order of magnitude faster in some cases, which shows
good potential in future realistic applications. 相似文献