High-order accurate monotone compact running scheme for multidimensional hyperbolic equations

Чикиткин, А. В.; Rogov, B. V.; Utyuzhnikov, Sergei

doi:10.1016/j.apnum.2014.02.008

Cited by 25 publications

(41 citation statements)

References 58 publications

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“…they coincide with orders in t and x of the linear advection equation (10). By difference order of a scheme in space we mean the difference between the number of stencil nodes in the x direction and the number of equations in the scheme.…”

Section: Fully Discrete Bicompact Schemesmentioning

confidence: 99%

“…This three-layer finite difference scheme was first proposed in [24]. In case of the linear advection equation (10) it is written as Fig. 9.…”

Section: Comparison Of Bicompact Schemes With Some Known Numerical Scmentioning

confidence: 99%

“…Below we present a Fourier analysis of the two fully discrete compact schemes C4-BE and C4-CN for the linear advection equation (10). The C4-BE scheme is constructed by applying the implicit Euler method for time integration in the semidiscrete scheme (54), and the C4-CN scheme -by applying the trapezoid rule [7] to it.…”

Section: Comparison Of Bicompact Schemes With Some Known Numerical Scmentioning

confidence: 99%

“…into numerical schemes for the advection equation (10). Here  is the so-called amplification factor [20][21][22] which is a complex number in general case,  is the absolute value of this factor.…”

Section: Fourier Analysis Of Fully Discrete Bicompact Schemesmentioning

confidence: 99%

“…Equations of the semi-discrete scheme are proposed to be integrated in time by multi-stage A-and L-stable diagonally implicit Runge-Kutta (RK) methods that are numerically efficient in comparison with fully implicit RK [7]. The scheme [6] was generalized for systems of equations and many space dimensions in [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations

Rogov

2018

KIAM Prepr.

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(Online) Rogov B.V.Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations Moscow -2018 Boris Vadimovich RogovDispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equationsThe Fourier analysis of fully discrete bicompact fourth-order spatial approximation schemes for hyperbolic equations is presented. This analysis is carried out on the example of a model linear advection equation. The results of Fourier analysis are presented as graphs of the dependence of the dispersion and dissipative characteristics of the bicompact schemes on the dimensionless wave number and the Courant number. The dispersion and dissipative properties of bicompact schemes are compared with those of other widely used difference schemes for hyperbolic equations. It is shown that bicompact schemes have one of the best spectral resolutions among the difference schemes being compared.

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Section: Fully Discrete Bicompact Schemesmentioning

confidence: 99%

“…This three-layer finite difference scheme was first proposed in [24]. In case of the linear advection equation (10) it is written as Fig. 9.…”

Section: Comparison Of Bicompact Schemes With Some Known Numerical Scmentioning

confidence: 99%

Section: Comparison Of Bicompact Schemes With Some Known Numerical Scmentioning

confidence: 99%

Section: Fourier Analysis Of Fully Discrete Bicompact Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations

Rogov

2018

KIAM Prepr.

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Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations

Rogov

2019

Applied Numerical Mathematics

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О р д е н а Л е н и н а ИНСТИТУТ ПРИКЛАДНОЙ МАТЕМАТИКИ имени М.В.Келдыша Р о с с и й с к о й а к а д е м и и н а у к Б.В.Рогов Дисперсионные и диссипативные свойства полностью дискретных бикомпактных схем четвертого порядка пространственной аппроксимации для уравнений гиперболического типа Москва-2018 Рогов Б.В. Дисперсионные и диссипативные свойства полностью дискретных бикомпактных схем четвертого порядка пространственной аппроксимации для уравнений гиперболического типа Представлен Фурье-анализ полностью дискретных бикомпактных схем четвертого порядка пространственной аппроксимации для уравнений гиперболического типа. Такой анализ проведен на примере модельного линейного уравнения переноса. Результаты Фурье-анализа представлены в виде графиков зависимости дисперсионных и диссипативных характеристик бикомпактных схем от безразмерного волнового числа и числа Куранта. Проведено сравнение дисперсионных и диссипативных свойств бикомпактных схем с аналогичными свойствами других широко используемых разностных схем для уравнений гиперболического типа. Показано, что бикомпактные схемы имеют одно из лучших спектральных разрешений среди сравниваемых разностных схем. Ключевые слова: уравнения гиперболического типа, бикомпактные схемы, дисперсия, диссипация Boris Vadimovich Rogov Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations The Fourier analysis of fully discrete bicompact fourth-order spatial approximation schemes for hyperbolic equations is presented. This analysis is carried out on the example of a model linear advection equation. The results of Fourier analysis are presented as graphs of the dependence of the dispersion and dissipative characteristics of the bicompact schemes on the dimensionless wave number and the Courant number. The dispersion and dissipative properties of bicompact schemes are compared with those of other widely used difference schemes for hyperbolic equations. It is shown that bicompact schemes have one of the best spectral resolutions among the difference schemes being compared.

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Family of central bicompact schemes with spectral resolution property for hyperbolic equations

Чикиткин

Rogov

2019

Applied Numerical Mathematics

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High-order accurate monotone compact running scheme for multidimensional hyperbolic equations

Cited by 25 publications

References 58 publications

Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations

Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations

Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations

Family of central bicompact schemes with spectral resolution property for hyperbolic equations

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