High Order Accuracy Optimized Methods for Constrained Numerical Solutions of Hyperbolic Conservation Laws

1994 ◽  
Vol 15 (4) ◽  
pp. 846-865
Author(s):  
C. Coray ◽  
J. Koebbe
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Numerical Solutions ◽  
High Order ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
Hyperbolic Conservation

scholarly journals Alternating Polynomial Reconstruction Method for Hyperbolic Conservation Laws

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1885
Author(s):  
Shijian Lin ◽  
Qi Luo ◽  
Hongze Leng ◽  
Junqiang Song
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Euler Method ◽  
High Order ◽  
High Order Accuracy ◽  
Reconstruction Method ◽  
Hyperbolic Conservation ◽  
High Order Schemes ◽  
Numerical Solver ◽  
Polynomial Reconstruction

We propose a new multi-moment numerical solver for hyperbolic conservation laws by using the alternating polynomial reconstruction approach. Unlike existing multi-moment schemes, our approach updates model variables by implementing two polynomial reconstructions alternately. First, Hermite interpolation reconstructs the solution within the cell by matching the point-based variables containing both physical values and their spatial derivatives. Then the reconstructed solution is updated by the Euler method. Second, we solve a constrained least-squares problem to correct the updated solution to preserve the conservation laws. Our method enjoys the advantages of a compact numerical stencil and high-order accuracy. Fourier analysis also indicates that our method allows a larger CFL number compared with many other high-order schemes. By adding a proper amount of artificial viscosity, shock waves and other discontinuities can also be computed accurately and sharply without solving an approximated Riemann problem.

A Compact High Order Space-Time Method for Conservation Laws

2011 ◽  
Vol 9 (2) ◽  
pp. 441-480 ◽  
Author(s):  
Shuangzhang Tu ◽  
Gordon W. Skelton ◽  
Qing Pang
Keyword(s):  
Conservation Laws ◽  
Discontinuous Galerkin ◽  
Hyperbolic Conservation Laws ◽  
Space Time ◽  
High Order ◽  
Basis Functions ◽  
High Order Accuracy ◽  
Time Step ◽  
Order Of Accuracy ◽  
Hyperbolic Conservation

AbstractThis 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 space-time 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.

scholarly journals High order explicit local time stepping methods for hyperbolic conservation laws

2020 ◽  
Vol 89 (324) ◽  
pp. 1807-1842
Author(s):  
Thi-Thao-Phuong Hoang ◽  
Lili Ju ◽  
Wei Leng ◽  
Zhu Wang
Keyword(s):  
Conservation Laws ◽  
Local Time ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Hyperbolic Conservation ◽  
Time Stepping ◽  
Local Time Stepping

scholarly journals A HIGH ORDER CENTRAL-UPWIND SCHEME FOR HYPERBOLIC CONSERVATION LAWS

2015 ◽  
Vol 5 (3) ◽  
pp. 453-464
Author(s):  
Xiaohan Cheng ◽  
◽  
Yufeng Nie ◽  
Jianhu Feng ◽  
Li Cai ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Upwind Scheme ◽  
Hyperbolic Conservation
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