This paper presents a novel high-order space-time method for hyperbolic conservation laws.Two important concepts,the staggered space-time mesh of the space-time conservation element/solution element(CE/SE)method and t...This paper presents a novel high-order space-time method for hyperbolic conservation laws.Two important concepts,the staggered space-time mesh of the space-time conservation element/solution element(CE/SE)method and the local discontinuous basis functions of the space-time discontinuous Galerkin(DG)finite element method,are the two key ingredients of the new scheme.The staggered spacetime mesh is constructed using the cell-vertex structure of the underlying spatial mesh.The universal definitions of CEs and SEs are independent of the underlying spatial mesh and thus suitable for arbitrarily unstructured meshes.The solution within each physical time step is updated alternately at the cell level and the vertex level.For this solution updating strategy and the DG ingredient,the new scheme here is termed as the discontinuous Galerkin cell-vertex scheme(DG-CVS).The high order of accuracy is achieved by employing high-order Taylor polynomials as the basis functions inside each SE.The present DG-CVS exhibits many advantageous features such as Riemann-solver-free,high-order accuracy,point-implicitness,compactness,and ease of handling boundary conditions.Several numerical tests including the scalar advection equations and compressible Euler equations will demonstrate the performance of the new method.展开更多
The space-time conservation element and solution element(CE/SE)method is proposed for solving a conservative interface-capturing reducedmodel of compressible two-fluid flows.The flow equations are the bulk equations,c...The space-time conservation element and solution element(CE/SE)method is proposed for solving a conservative interface-capturing reducedmodel of compressible two-fluid flows.The flow equations are the bulk equations,combined with mass and energy equations for one of the two fluids.The latter equation contains a source term for accounting the energy exchange.The one and two-dimensional flow models are numerically investigated in this manuscript.The CE/SE method is capable to accurately capture the sharp propagating wavefronts of the fluids without excessive numerical diffusion or spurious oscillations.In contrast to the existing upwind finite volume schemes,the Riemann solver and reconstruction procedure are not the building block of the suggested method.The method differs from the previous techniques because of global and local flux conservation in a space-time domain without resorting to interpolation or extrapolation.In order to reveal the efficiency and performance of the approach,several numerical test cases are presented.For validation,the results of the current method are compared with other finite volume schemes.展开更多
基金This work is supported by the U.S.Air Force Office of Scientific Research(AFOSR)Computational Mathematics Program under the Award No.FA9550-08-1-0122.
文摘This paper presents a novel high-order space-time method for hyperbolic conservation laws.Two important concepts,the staggered space-time mesh of the space-time conservation element/solution element(CE/SE)method and the local discontinuous basis functions of the space-time discontinuous Galerkin(DG)finite element method,are the two key ingredients of the new scheme.The staggered spacetime mesh is constructed using the cell-vertex structure of the underlying spatial mesh.The universal definitions of CEs and SEs are independent of the underlying spatial mesh and thus suitable for arbitrarily unstructured meshes.The solution within each physical time step is updated alternately at the cell level and the vertex level.For this solution updating strategy and the DG ingredient,the new scheme here is termed as the discontinuous Galerkin cell-vertex scheme(DG-CVS).The high order of accuracy is achieved by employing high-order Taylor polynomials as the basis functions inside each SE.The present DG-CVS exhibits many advantageous features such as Riemann-solver-free,high-order accuracy,point-implicitness,compactness,and ease of handling boundary conditions.Several numerical tests including the scalar advection equations and compressible Euler equations will demonstrate the performance of the new method.
基金supported by Higher Education Commission(HEC)of Pakistan through grant No.1375.
文摘The space-time conservation element and solution element(CE/SE)method is proposed for solving a conservative interface-capturing reducedmodel of compressible two-fluid flows.The flow equations are the bulk equations,combined with mass and energy equations for one of the two fluids.The latter equation contains a source term for accounting the energy exchange.The one and two-dimensional flow models are numerically investigated in this manuscript.The CE/SE method is capable to accurately capture the sharp propagating wavefronts of the fluids without excessive numerical diffusion or spurious oscillations.In contrast to the existing upwind finite volume schemes,the Riemann solver and reconstruction procedure are not the building block of the suggested method.The method differs from the previous techniques because of global and local flux conservation in a space-time domain without resorting to interpolation or extrapolation.In order to reveal the efficiency and performance of the approach,several numerical test cases are presented.For validation,the results of the current method are compared with other finite volume schemes.
