On two upwind finite-difference schemes for hyperbolic equations in non-conservative form

Gabutti, Bruno

doi:10.1016/0045-7930(83)90031-2

Cited by 48 publications

(16 citation statements)

References 15 publications

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“…The constraint prescribing a total temperature T o constant in time is: 4) and can be linearized in time as: 5) and then expressed in terms of the thermodynamic unknowns a and s:…”

Section: Total Temperature Constant In Timementioning

confidence: 99%

“…The computational efficiency of the original λ scheme is poor and the scheme has to be modified near the boundaries. Gabutti [4] developed a class of second-order characteristic-biased schemes that contains, as particular case, the λ scheme, but also more efficient two-step procedures. Among these, Gabutti rediscovered the scheme proposed by Zhu Youlan et al [5], which, with minor modifications, substituted the original λ scheme [1].…”

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confidence: 99%

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On the numerical integration of multi-dimensional, initial boundary value problems for the Euler equations in quasi-linear form

Valorani

Favini

1998

Numer. Methods Partial Differential Eq.

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A matricial formalism to solve multi-dimensional initial boundary values problems for hyperbolic equations written in quasi-linear based on the λ scheme approach is presented. The derivation is carried out for nonorthogonal, moving systems of curvilinear coordinates. A uniform treatment of the integration at the boundaries, when the boundary conditions can be expressed in terms of combinations of time or space derivatives of the primitive variables, is also presented. The methodology is validated against a two-dimensional test case, the supercritical flow through the Hobson cascade n.2, and in three-dimensional test cases such as the supersonic flow about a sphere and the flow through a plug nozzle.

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“…The constraint prescribing a total temperature T o constant in time is: 4) and can be linearized in time as: 5) and then expressed in terms of the thermodynamic unknowns a and s:…”

Section: Total Temperature Constant In Timementioning

confidence: 99%

mentioning

confidence: 99%

On the numerical integration of multi-dimensional, initial boundary value problems for the Euler equations in quasi-linear form

Valorani

Favini

1998

Numer. Methods Partial Differential Eq.

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“…(1, I+)T, (1, UT, (27) the superscript T denotes transpose and 2 = @/ap is the square of the speed of sound. Therefore, (25) is hyperbolic and the boundary conditions at f = 0 and Z= LIDH here referred to as inflow and outflow, respectively, are determined from the number of characteristics entering into the flow field at these boundaries.…”

Section: Boundary Conditionsmentioning

confidence: 99%

One‐dimensional, time‐dependent, homogeneous, two‐phase flow in volcanic conduits

Ramos

1995

Numerical Methods in Fluids

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SUMMARYA one-dimensional, time-dependent, isothermal, homogeneous, two-phase flow model was developed to study magma ascent in volcanic conduits. The physical modeling equations were numerically solved by means of a TVD (total variation diminishing) predictor-corrector procedure and by means of a predictor-corrector technique based on the method of characteristics. The results from the transient model were verified with an analytical solution for wave propagation in conduits without friction and gravitational effects. The numerical solutions were also compared with those of a steady-state, homogeneous, two-phase model for basaltic and rhyolitic magma ascents in the fissures and circular conduits of Vesuvius and Mt St. Helens. An application of the model to magma decompression in conduits indicates very short times for gas exsolution, fragmentation, and shock wave propagation, implying that the modelling of gas exsolution should involve non-equilibrium kinetics effects. Future coupling of the transient magma ascent model with magma chamber and pyroclastic dispersion models should allow for more realistic simulations of the time-dependent behavior of real volcanic eruptions.

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“…The fixed indices have been omitted in this expression. For second-order accuracy, we use Gabutti's three-step scheme 19 : first-order one-sided finite differences, Eq. (18), in the predictor and final steps, and the first-order difference formula $*/= =F?//±3/-±1=F/-±2 in the intermediate step.…”

Section: Numerical Schemementioning

confidence: 99%

Finite-difference method-of-characteristics scheme for the equationsof gasdynamics

Parpia

1991

AIAA Journal

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A finite-difference method for the characteristic equations of gasdynamics is developed. The method is based on a directed discretization of the characteristic compatibility conditions. The choice of wave propagation directions is arbitrary, and there is no need to fit interpolating functions to the initial data. The proposed method is not conservative and therefore must be used with a shock-fitting procedure in regions wherever the flow is discontinuous. Numerical results are presented for sample two-dimensional problems.

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On two upwind finite-difference schemes for hyperbolic equations in non-conservative form

Cited by 48 publications

References 15 publications

On the numerical integration of multi-dimensional, initial boundary value problems for the Euler equations in quasi-linear form

On the numerical integration of multi-dimensional, initial boundary value problems for the Euler equations in quasi-linear form

One‐dimensional, time‐dependent, homogeneous, two‐phase flow in volcanic conduits

Finite-difference method-of-characteristics scheme for the equationsof gasdynamics

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