A class of finite difference Hermite radial basis functions weighted essentially non-oscillatory(HRWENO)methods for solving conservation laws was presented by Abedian(Int.J.Numer.Meth.Fluids,94(2022),pp.583-607).To re...A class of finite difference Hermite radial basis functions weighted essentially non-oscillatory(HRWENO)methods for solving conservation laws was presented by Abedian(Int.J.Numer.Meth.Fluids,94(2022),pp.583-607).To reconstruct the fluxes in HRWENO,the common practice of reconstructing the flux functions was employed.In this follow-up research work,an alternative formulation to reconstruct the numerical fluxes is considered.First,the solution and its derivatives are directly employed to interpolate point values at interfaces of computational cells.Afterwards,the point values at interface of cell in building block are considered to obtain numerical fluxes.In this framework,arbitrary monotone fluxes can be employed,while in HRWENO the classical practice of reconstructing flux functions can be considered only to smooth flux splitting.Also,in the process of reconstruction these type of schemes consider the effectively narrower stencil of HRWENO methods.Extensive test cases such as Euler equations of compressible gas dynamics are considered to show the good performance of the methods.展开更多
A moving collocation method has been shown to be very effcient for the adaptive solution of second- and fourth-order time-dependent partial differential equations and forms the basis for the two robust codes MOVCOL an...A moving collocation method has been shown to be very effcient for the adaptive solution of second- and fourth-order time-dependent partial differential equations and forms the basis for the two robust codes MOVCOL and MOVCOL4. In this paper, the relations between the method and the traditional collocation and finite volume methods are investigated. It is shown that the moving collocation method inherits desirable properties of both methods： the ease of implementation and high-order convergence of the traditional collocation method and the mass conservation of the finite volume method. Convergence of the method in the maximum norm is proven for general linear two-point boundary value problems. Numerical results are given to demonstrate the convergence order of the method.展开更多
文摘A class of finite difference Hermite radial basis functions weighted essentially non-oscillatory(HRWENO)methods for solving conservation laws was presented by Abedian(Int.J.Numer.Meth.Fluids,94(2022),pp.583-607).To reconstruct the fluxes in HRWENO,the common practice of reconstructing the flux functions was employed.In this follow-up research work,an alternative formulation to reconstruct the numerical fluxes is considered.First,the solution and its derivatives are directly employed to interpolate point values at interfaces of computational cells.Afterwards,the point values at interface of cell in building block are considered to obtain numerical fluxes.In this framework,arbitrary monotone fluxes can be employed,while in HRWENO the classical practice of reconstructing flux functions can be considered only to smooth flux splitting.Also,in the process of reconstruction these type of schemes consider the effectively narrower stencil of HRWENO methods.Extensive test cases such as Euler equations of compressible gas dynamics are considered to show the good performance of the methods.
基金supported by Natural Sciences and Engineering Research Council of Canada (Grant No. A8781)National Natural Science Foundation of China (Grant No. 11171274)National Science Foundation of USA (Grant No. DMS-0712935)
文摘A moving collocation method has been shown to be very effcient for the adaptive solution of second- and fourth-order time-dependent partial differential equations and forms the basis for the two robust codes MOVCOL and MOVCOL4. In this paper, the relations between the method and the traditional collocation and finite volume methods are investigated. It is shown that the moving collocation method inherits desirable properties of both methods： the ease of implementation and high-order convergence of the traditional collocation method and the mass conservation of the finite volume method. Convergence of the method in the maximum norm is proven for general linear two-point boundary value problems. Numerical results are given to demonstrate the convergence order of the method.
