We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 198...We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 1983 HLL Riemann solver. We de- velop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids. We apply a composite scheme that uses a Lax- Friedrichs time step as a dissipative filter after several Lax-Wendroff time steps. Numerical results for Noh＇s infinite strength shock problem, the Sedov blast wave problem, and the Saltzman piston problem are presented.展开更多
The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems.The preservation of the qualitative characteristics,such as the maximum principle,in discrete mode...The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems.The preservation of the qualitative characteristics,such as the maximum principle,in discrete model is one of the key requirements.It is well known that standard linear finite element solution does not satisfy maximum principle on general triangular meshes in 2D.In this paper we consider how to enforce discrete maximum principle for linear finite element solutions for the linear second-order self-adjoint elliptic equation.First approach is based on repair technique,which is a posteriori correction of the discrete solution.Second method is based on constrained optimization.Numerical tests that include anisotropic cases demonstrate how our method works for problems for which the standard finite element methods produce numerical solutions that violate the discrete maximum principle.展开更多
The second and final year of the Erasmus Plus programme’Innovative Education and Training in high power laser plasmas’,otherwise known as PowerLaPs,is described.The PowerLaPs programme employs an innovative paradigm...The second and final year of the Erasmus Plus programme’Innovative Education and Training in high power laser plasmas’,otherwise known as PowerLaPs,is described.The PowerLaPs programme employs an innovative paradigm in that it is a multi-centre programme,where teaching takes place in five separate institutes with a range of different aims and styles of delivery.The’in-class’time is limited to 4 weeks a year,and the programme spans 2 years.PowerLaPs aims to train students from across Europe in theoretical,applied and laboratory skills relevant to the pursuit of research in laser plasma interaction physics and inertial confinement fusion.Lectures are intermingled with laboratory sessions and continuous assessment activities.The programme,which is led by workers from the Hellenic Mediterranean University and supported by co-workers from the Queen’s University Belfast,the University of Bordeaux,the Czech Technical University in Prague,Ecole Polytechnique,the University of Ioannina,the University of Salamanca and the University of York,has just finished its second and final year.Six Learning Teaching Training activities have been held at the Queen’s University Belfast,the University of Bordeaux,the Czech Technical University,the University of Salamanca and the Institute of Plasma Physics and Lasers of the Hellenic Mediterranean University.The last of these institutes hosted two 2-week-long Intensive Programmes,while the activities at the other four universities were each 5 days in length.In addition,a’Multiplier Event’was held at the University of Ioannina,which will be briefly described.In this second year,the work has concentrated on training in both experimental diagnostics and simulation techniques appropriate to the study of plasma physics,high power laser matter interactions and high energy density physics.The nature of the programme will be described in detail,and some metrics relating to the activities carried out will be presented.In particular,this paper will focus on the overall assessment of the programme.展开更多
基金performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No.DE-AC52-06NA25396supported in part by the Czech Science Foundation GrantP205/10/0814the Czech Ministry of Education grants MSM 6840770022 and LC528
文摘We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 1983 HLL Riemann solver. We de- velop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids. We apply a composite scheme that uses a Lax- Friedrichs time step as a dissipative filter after several Lax-Wendroff time steps. Numerical results for Noh＇s infinite strength shock problem, the Sedov blast wave problem, and the Saltzman piston problem are presented.
基金the National Nuclear Security Administration of the U.S.Department of Energy at Los Alamos National Laboratory under Contract No.DE-AC52-06NA25396the DOE Office of Science Advanced Scientific Computing Research(ASCR)Program in Applied Mathematics Research.The first author has been supported in part by the Czech Ministry of Education projects MSM 6840770022 and LC06052(Necas Center for Mathematical Modeling).
文摘The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems.The preservation of the qualitative characteristics,such as the maximum principle,in discrete model is one of the key requirements.It is well known that standard linear finite element solution does not satisfy maximum principle on general triangular meshes in 2D.In this paper we consider how to enforce discrete maximum principle for linear finite element solutions for the linear second-order self-adjoint elliptic equation.First approach is based on repair technique,which is a posteriori correction of the discrete solution.Second method is based on constrained optimization.Numerical tests that include anisotropic cases demonstrate how our method works for problems for which the standard finite element methods produce numerical solutions that violate the discrete maximum principle.
基金the financial support of the Erasmus Plus and the IKY/Erasmus+Hellenic National Agencythe support of the administrative teams of the universities involved in PowerLaPs+3 种基金support by computational time granted from the Greek Research and Technology Network(GRNET)in the National HPC facility ARIS under project ID pr007020 LaMIPlaS-IIsupport by‘ELILASERLAB Europe Synergy,HiPER and IPERION-CH.gr’(MIS 5002735),which is implemented under the Action‘Reinforcement of the Research and Innovation Infrastructure’funded by the Operational Programme‘Competitiveness,Entrepreneurship and Innovation’(NSRF 2014-2020)co-financed by Greece and the European Union(European Regional Development Fund)。
文摘The second and final year of the Erasmus Plus programme’Innovative Education and Training in high power laser plasmas’,otherwise known as PowerLaPs,is described.The PowerLaPs programme employs an innovative paradigm in that it is a multi-centre programme,where teaching takes place in five separate institutes with a range of different aims and styles of delivery.The’in-class’time is limited to 4 weeks a year,and the programme spans 2 years.PowerLaPs aims to train students from across Europe in theoretical,applied and laboratory skills relevant to the pursuit of research in laser plasma interaction physics and inertial confinement fusion.Lectures are intermingled with laboratory sessions and continuous assessment activities.The programme,which is led by workers from the Hellenic Mediterranean University and supported by co-workers from the Queen’s University Belfast,the University of Bordeaux,the Czech Technical University in Prague,Ecole Polytechnique,the University of Ioannina,the University of Salamanca and the University of York,has just finished its second and final year.Six Learning Teaching Training activities have been held at the Queen’s University Belfast,the University of Bordeaux,the Czech Technical University,the University of Salamanca and the Institute of Plasma Physics and Lasers of the Hellenic Mediterranean University.The last of these institutes hosted two 2-week-long Intensive Programmes,while the activities at the other four universities were each 5 days in length.In addition,a’Multiplier Event’was held at the University of Ioannina,which will be briefly described.In this second year,the work has concentrated on training in both experimental diagnostics and simulation techniques appropriate to the study of plasma physics,high power laser matter interactions and high energy density physics.The nature of the programme will be described in detail,and some metrics relating to the activities carried out will be presented.In particular,this paper will focus on the overall assessment of the programme.
