We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations ...We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.展开更多
The synthesis of gold nanoparticles(Au NPs)was carried out by utilising the pulsed laser ablation in liquids(PLAL)method with a microchip laser(MCL)system.This portable system features low power consumption and a gian...The synthesis of gold nanoparticles(Au NPs)was carried out by utilising the pulsed laser ablation in liquids(PLAL)method with a microchip laser(MCL)system.This portable system features low power consumption and a giant-pulse laser.Aqueous solutions with and without the surfactant poly(N-vinyl-2-pyrrolidone)(PVP)were used for laser ablation of a bulk gold rod to achieve the successful formation of a colloidal solution of Au NPs.The gas bubbles formed by heating the aqueous medium around the surface of the gold target significantly reduced the efficiency of Au NP ablation.This effect was more pronounced and prolonged in high-viscosity solutions,hindering energy transfer from subsequent laser pulses to the target.Additionally,it was suggested that the chain length of PVP does not affect either the size of the Au NPs or the ablation efficiency.Videography experiments were conducted to explore the ablation mechanism employed by the MCL system.The relatively short pulse duration of the MCL system may contribute to the formation of NPs with consistent size,which were suppressed to grow in significantly smaller cavitation bubbles with short lifetimes.展开更多
文摘We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.
基金supported by JSPS KAKENHI(JP19K22187)Foundation for the Promotion of Science&Engineering for financial supportthe Japan International Cooperation Agency(JICA)and Otsuka Toshimi Scholarship Foundation(21-S58 and 22-S30)for kindly providing scholarships.
文摘The synthesis of gold nanoparticles(Au NPs)was carried out by utilising the pulsed laser ablation in liquids(PLAL)method with a microchip laser(MCL)system.This portable system features low power consumption and a giant-pulse laser.Aqueous solutions with and without the surfactant poly(N-vinyl-2-pyrrolidone)(PVP)were used for laser ablation of a bulk gold rod to achieve the successful formation of a colloidal solution of Au NPs.The gas bubbles formed by heating the aqueous medium around the surface of the gold target significantly reduced the efficiency of Au NP ablation.This effect was more pronounced and prolonged in high-viscosity solutions,hindering energy transfer from subsequent laser pulses to the target.Additionally,it was suggested that the chain length of PVP does not affect either the size of the Au NPs or the ablation efficiency.Videography experiments were conducted to explore the ablation mechanism employed by the MCL system.The relatively short pulse duration of the MCL system may contribute to the formation of NPs with consistent size,which were suppressed to grow in significantly smaller cavitation bubbles with short lifetimes.
