Construction of High Order Accuracy Decomposition Scheme for an Abstract Hyperbolic Equation with the Lipschitz Continuous Operator on the Basis of Rational Splitting of the Cosine-Operator Function

2011 ◽  
Author(s):  
J. Rogava ◽  
M. Tsiklauri ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Hyperbolic Equation ◽  
Operator Function ◽  
Continuous Operator ◽  
High Order ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
Cosine Operator Function ◽  
Lipschitz Continuous ◽  
Decomposition Scheme ◽  
Lipschitz Continuous Operator

Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation

2018 ◽  
Vol 25 (3) ◽  
pp. 337-348
Author(s):  
Nana Dikhaminjia ◽  
Jemal Rogava ◽  
Mikheil Tsiklauri
Keyword(s):  
Approximate Solution ◽  
Evolution Equation ◽  
Continuous Operator ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
Lipschitz Continuous ◽  
Decomposition Scheme ◽  
Linear Evolution ◽  
Numerical Resolution ◽  
Linear Evolution Equation

AbstractIn the present work the Cauchy problem for an abstract evolution equation with a Lipschitz-continuous operator is considered, where the main operator represents the sum of positive definite self-adjoint operators. The fourth-order accuracy decomposition scheme is constructed for an approximate solution of the problem. The theorem on the error estimate of an approximate solution is proved. Numerical calculations for different model problems are carried out using the constructed scheme. The obtained numerical results confirm the theoretical conclusions.

The Fourth Order of Accuracy Decomposition Scheme for Abstract Hyperbolic Equation

2008 ◽  
Vol 15 (1) ◽  
pp. 165-175
Author(s):  
Jemal Rogava ◽  
Mikheil Tsiklauri
Keyword(s):  
Approximate Solution ◽  
Hyperbolic Equation ◽  
Fourth Order ◽  
Operator Function ◽  
Order Accuracy ◽  
Order Of Accuracy ◽  
Cosine Operator Function ◽  
Decomposition Scheme ◽  
Cosine Operator ◽  
Abstract Hyperbolic Equation

Abstract Using the rational splitting of a cosine operator-function, the fourth order accuracy decomposition scheme is constructed for hyperbolic equation when the principal operator is self-adjoint positively defined and is represented as a sum of two summands. Stability of the constructed scheme is shown and the error of an approximate solution is estimated.

scholarly journals High-Order Hybrid WCNS-CPR Scheme for Shock Capturing of Conservation Laws

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jia Guo ◽  
Huajun Zhu ◽  
Zhen-Guo Yan ◽  
Lingyan Tang ◽  
Songhe Song
Keyword(s):  
Computational Cost ◽  
High Order ◽  
Shock Capturing ◽  
High Order Accuracy ◽  
Hybrid Technique ◽  
Hybrid Scheme ◽  
Order Accuracy ◽  
Order Of Accuracy ◽  
Reconstruction Scheme ◽  
High Gradients

By introducing hybrid technique into high-order CPR (correction procedure via reconstruction) scheme, a novel hybrid WCNS-CPR scheme is developed for efficient supersonic simulations. Firstly, a shock detector based on nonlinear weights is used to identify grid cells with high gradients or discontinuities throughout the whole flow field. Then, WCNS (weighted compact nonlinear scheme) is adopted to capture shocks in these areas, while the smooth area is calculated by CPR. A strategy to treat the interfaces of the two schemes is developed, which maintains high-order accuracy. Convergent order of accuracy and shock-capturing ability are tested in several numerical experiments; the results of which show that this hybrid scheme achieves expected high-order accuracy and high resolution, is robust in shock capturing, and has less computational cost compared to the WCNS.

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