We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations.High accuracy(up to the sixth-order ...We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations.High accuracy(up to the sixth-order presently)is achieved,thanks to polynomial recon-structions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of dis-continuities.We supplemented this scheme with a stencil construction allowing to reduce even further the numerical dissipation.The stencil is shifted away from troubles(shocks,discontinuities,etc.)leading to less oscillating polynomial reconstructions.Experimented on linear,Burgers',and Euler equations,we demonstrate that the adaptive stencil technique manages to retrieve smooth solutions with optimal order of accuracy but also irregular ones without spurious oscillations.Moreover,we numerically show that the approach allows to reduce the dissipation still maintaining the essentially non-oscillatory behavior.展开更多
The study of earth masses requires numerical methods that provide the quantification of the safety factor without requiring detrimental assumptions. For that, equilibrium analysis can perform fast computations but req...The study of earth masses requires numerical methods that provide the quantification of the safety factor without requiring detrimental assumptions. For that, equilibrium analysis can perform fast computations but require assumptions that limit its potentiality. Limit analysis does not require detrimental assumptions but are numerically demanding. This work provides a new approach that combines the advantage of both the equilibrium method and the limit analysis. The defined hybrid model allows probabilistic analysis and optimization approaches without the assumption of interslice forces. It is compared with a published case and used to perform probabilistic studies in both a homogeneous and a layered foundation. Analyses show that the shape of the density probability functions is highly relevant when computing the probability of failure, and soil elasticity hardly affects the safety of factor of the earth mass.展开更多
基金support by FEDER-Fundo Europeu de Desenvolvimento Regional,through COMPETE 2020-Programa Operational Fatores de Competitividade,and the National Funds through FCT-Fundacao para a Ciencia e a Tecnologia,project no.UID/FIS/04650/2019support by FEDER-Fundo Europeu de Desenvolvimento Regional,through COMPETI E 2020-Programa Operacional Fatores de Competitividade,and the National Funds through FCT-Fundacao para a Ciencia e a Tecnologia,project no.POCI-01-0145-FEDER-028118
文摘We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations.High accuracy(up to the sixth-order presently)is achieved,thanks to polynomial recon-structions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of dis-continuities.We supplemented this scheme with a stencil construction allowing to reduce even further the numerical dissipation.The stencil is shifted away from troubles(shocks,discontinuities,etc.)leading to less oscillating polynomial reconstructions.Experimented on linear,Burgers',and Euler equations,we demonstrate that the adaptive stencil technique manages to retrieve smooth solutions with optimal order of accuracy but also irregular ones without spurious oscillations.Moreover,we numerically show that the approach allows to reduce the dissipation still maintaining the essentially non-oscillatory behavior.
基金founded by FEDER Funds through Programa Operacional Factores de Competitividade-COMPETEby Portuguese Funds through FCT–Fundacao para a Ciencia e a Tecnologiathe projects PEst –C/MAT/UI0013/2011 and PEst–OE/ECM/UI4047/2011
文摘The study of earth masses requires numerical methods that provide the quantification of the safety factor without requiring detrimental assumptions. For that, equilibrium analysis can perform fast computations but require assumptions that limit its potentiality. Limit analysis does not require detrimental assumptions but are numerically demanding. This work provides a new approach that combines the advantage of both the equilibrium method and the limit analysis. The defined hybrid model allows probabilistic analysis and optimization approaches without the assumption of interslice forces. It is compared with a published case and used to perform probabilistic studies in both a homogeneous and a layered foundation. Analyses show that the shape of the density probability functions is highly relevant when computing the probability of failure, and soil elasticity hardly affects the safety of factor of the earth mass.
