A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapp...A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV,M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.展开更多
Compared with vertical and horizontal wells, the solution and computation of transient pressure responses of slanted wells are more complex. Vertical and horizontal wells are both simplified cases of slanted wells at ...Compared with vertical and horizontal wells, the solution and computation of transient pressure responses of slanted wells are more complex. Vertical and horizontal wells are both simplified cases of slanted wells at particular inclination, so the model for slanted wells is more general and more complex than other models for vertical and horizontal wells. Many authors have studied unsteady-state flow of fluids in slanted wells and various solutions have been proposed. However, until now, few of the published results pertain to the computational efficiency. Whether in the time domain or in the Laplace domain, the computation of integration of complex functions is necessary in obtaining pressure responses of slanted wells, while the computation of the integration is complex and time-consuming. To obtain a perfect type curve the computation time is unacceptable even with an aid of high-speed computers. The purpose of this paper is to present an efficient algorithm to compute transient pressure distributions caused by slanted wells in reservoirs. Based on rigorous derivation, the transient pressure solution for slanted wells of any inclination angle is presented. Assuming an infinite-conductivity wellbore, the location of the equivalent-pressure point is determined. More importantly, according to the characteristics of the integrand in a transient pressure solution for slanted wells, the whole integral interval is partitioned into several small integral intervals, and then the method of variable substitution and the variable step-size piecewise numerical integration are employed. The amount of computation is significantly reduced and the computational efficiency is greatly improved. The algorithm proposed in this paper thoroughly solved the difficulty in the efficient and high-speed computation of transient pressure distribution of slanted wells with any inclination angle.展开更多
We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity mod...We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity modified by some smoothing,which is found to con-siderably reduce the numerical dissipation introduced by Riemann solvers.The scheme preserves constant states for any mesh motion and we also study its positivity preservation property.Local grid refinement and coarsening are performed to maintain the mesh qual-ity and avoid the appearance of very small or large cells.Second,higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.展开更多
In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing ac...In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing accuracy-conserving(SIAC)filter is a post-processing technique to enhance the accuracy of the discontinuous Galerkin(DG)solutions.This work is the essential step to extend the SIAC filter to the moving mesh for nonlinear problems.By the post-processing theory,the negative norm estimates are vital to get the superconvergence error estimates of the solutions after post-processing in the L2 norm.Although the SIAC filter has been extended to nonuniform mesh,the analysis of fil-tered solutions on the nonuniform mesh is complicated.We prove superconvergence error estimates in the negative norm for the ALE-DG method on moving meshes.The main dif-ficulties of the analysis are the terms in the ALE-DG scheme brought by the grid velocity field,and the time-dependent function space.The mapping from time-dependent cells to reference cells is very crucial in the proof.The numerical results also confirm the theoreti-cal proof.展开更多
A memory compress algorithm for 12\|bit Arbitrary Waveform Generator (AWG) is presented and optimized. It can compress waveform memory for a sinusoid to 16×13bits with a Spurious Free Dynamic Range (SFDR) 90.7dBc...A memory compress algorithm for 12\|bit Arbitrary Waveform Generator (AWG) is presented and optimized. It can compress waveform memory for a sinusoid to 16×13bits with a Spurious Free Dynamic Range (SFDR) 90.7dBc (1/1890 of uncompressed memory at the same SFDR) and to 8×12bits with a SFDR 79dBc. Its hardware cost is six adders and two multipliers. Exploiting this memory compress technique makes it possible to build a high performance AWG on a chip.展开更多
In this paper,several arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)methods are presented for Korteweg-de Vries(KdV)type equations on moving meshes.Based on the L^(2) conservation law of KdV equations,we...In this paper,several arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)methods are presented for Korteweg-de Vries(KdV)type equations on moving meshes.Based on the L^(2) conservation law of KdV equations,we adopt the conservative and dissipative numerical fuxes for the nonlinear convection and linear dispersive terms,respectively.Thus,one conservative and three dissipative ALE-DG schemes are proposed for the equations.The invariant preserving property for the conservative scheme and the corresponding dissipative properties for the other three dissipative schemes are all presented and proved in this paper.In addition,the L^(2)-norm error estimates are also proved for two schemes,whose numerical fuxes for the linear dispersive term are both dissipative type.More precisely,when choosing the approximation space with the piecewise kth degree polynomials,the error estimate provides the kth order of convergence rate in L^(2)-norm for the scheme with the conservative numerical fuxes applied for the nonlinear convection term.Furthermore,the(k+1∕2)th order of accuracy can be proved for the ALE-DG scheme with dissipative numerical fuxes applied for the convection term.Moreover,a Hamiltonian conservative ALE-DG scheme is also presented based on the conservation of the Hamiltonian for KdV equations.Numerical examples are shown to demonstrate the accuracy and capability of the moving mesh ALE-DG methods and compare with stationary DG methods.展开更多
An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuou...An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.展开更多
基金Project supported by the China Postdoctoral Science Foundation(No.2017M610823)
文摘A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV,M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.
基金financial support from the special fund of China’s central government for the development of local colleges and universities―the project of national first-level discipline in Oil and Gas Engineering, the National Science Fund for Distinguished Young Scholars of China (Grant No. 51125019)the National Program on Key fundamental Research Project (973 Program, Grant No. 2011CB201005)
文摘Compared with vertical and horizontal wells, the solution and computation of transient pressure responses of slanted wells are more complex. Vertical and horizontal wells are both simplified cases of slanted wells at particular inclination, so the model for slanted wells is more general and more complex than other models for vertical and horizontal wells. Many authors have studied unsteady-state flow of fluids in slanted wells and various solutions have been proposed. However, until now, few of the published results pertain to the computational efficiency. Whether in the time domain or in the Laplace domain, the computation of integration of complex functions is necessary in obtaining pressure responses of slanted wells, while the computation of the integration is complex and time-consuming. To obtain a perfect type curve the computation time is unacceptable even with an aid of high-speed computers. The purpose of this paper is to present an efficient algorithm to compute transient pressure distributions caused by slanted wells in reservoirs. Based on rigorous derivation, the transient pressure solution for slanted wells of any inclination angle is presented. Assuming an infinite-conductivity wellbore, the location of the equivalent-pressure point is determined. More importantly, according to the characteristics of the integrand in a transient pressure solution for slanted wells, the whole integral interval is partitioned into several small integral intervals, and then the method of variable substitution and the variable step-size piecewise numerical integration are employed. The amount of computation is significantly reduced and the computational efficiency is greatly improved. The algorithm proposed in this paper thoroughly solved the difficulty in the efficient and high-speed computation of transient pressure distribution of slanted wells with any inclination angle.
文摘We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity modified by some smoothing,which is found to con-siderably reduce the numerical dissipation introduced by Riemann solvers.The scheme preserves constant states for any mesh motion and we also study its positivity preservation property.Local grid refinement and coarsening are performed to maintain the mesh qual-ity and avoid the appearance of very small or large cells.Second,higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.
基金the fellowship of China Postdoctoral Science Foundation,no:2020TQ0030.Y.Xu:Research supported by National Numerical Windtunnel Project NNW2019ZT4-B08+1 种基金Science Challenge Project TZZT2019-A2.3NSFC Grants 11722112,12071455.X.Li:Research supported by NSFC Grant 11801062.
文摘In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing accuracy-conserving(SIAC)filter is a post-processing technique to enhance the accuracy of the discontinuous Galerkin(DG)solutions.This work is the essential step to extend the SIAC filter to the moving mesh for nonlinear problems.By the post-processing theory,the negative norm estimates are vital to get the superconvergence error estimates of the solutions after post-processing in the L2 norm.Although the SIAC filter has been extended to nonuniform mesh,the analysis of fil-tered solutions on the nonuniform mesh is complicated.We prove superconvergence error estimates in the negative norm for the ALE-DG method on moving meshes.The main dif-ficulties of the analysis are the terms in the ALE-DG scheme brought by the grid velocity field,and the time-dependent function space.The mapping from time-dependent cells to reference cells is very crucial in the proof.The numerical results also confirm the theoreti-cal proof.
文摘A memory compress algorithm for 12\|bit Arbitrary Waveform Generator (AWG) is presented and optimized. It can compress waveform memory for a sinusoid to 16×13bits with a Spurious Free Dynamic Range (SFDR) 90.7dBc (1/1890 of uncompressed memory at the same SFDR) and to 8×12bits with a SFDR 79dBc. Its hardware cost is six adders and two multipliers. Exploiting this memory compress technique makes it possible to build a high performance AWG on a chip.
基金This work was supported by the National Numerical Windtunnel Project NNW2019ZT4-B08Science Challenge Project TZZT2019-A2.3the National Natural Science Foundation of China Grant no.11871449.
文摘In this paper,several arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)methods are presented for Korteweg-de Vries(KdV)type equations on moving meshes.Based on the L^(2) conservation law of KdV equations,we adopt the conservative and dissipative numerical fuxes for the nonlinear convection and linear dispersive terms,respectively.Thus,one conservative and three dissipative ALE-DG schemes are proposed for the equations.The invariant preserving property for the conservative scheme and the corresponding dissipative properties for the other three dissipative schemes are all presented and proved in this paper.In addition,the L^(2)-norm error estimates are also proved for two schemes,whose numerical fuxes for the linear dispersive term are both dissipative type.More precisely,when choosing the approximation space with the piecewise kth degree polynomials,the error estimate provides the kth order of convergence rate in L^(2)-norm for the scheme with the conservative numerical fuxes applied for the nonlinear convection term.Furthermore,the(k+1∕2)th order of accuracy can be proved for the ALE-DG scheme with dissipative numerical fuxes applied for the convection term.Moreover,a Hamiltonian conservative ALE-DG scheme is also presented based on the conservation of the Hamiltonian for KdV equations.Numerical examples are shown to demonstrate the accuracy and capability of the moving mesh ALE-DG methods and compare with stationary DG methods.
基金supported in part by a“Computational R&D in Support of Stockpile Stewardship”Grant from Lawrence Livermore National Laboratorythe National Science Foundation Grants DMS-1619892+2 种基金the Air Force Office of Scientifc Research,USAF,under Grant/contract number FA9955012-0358the Army Research Office under Grant/contract number W911NF-15-1-0517the Spanish MCINN under Project PGC2018-097565-B-I00
文摘An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.