Analytical and numerical solutions for carbonated waterflooding

Alvarez, Alex; Bruining, J.; Lambert, Wanderson; Marchesin, D.

doi:10.1007/s10596-017-9707-3

Cited by 6 publications

(4 citation statements)

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“…In this section we exemplify the appearance of coincidence locus with the model studied in [2]. The procedure developed in this paper is used to solve a particular Riemann problem.…”

Section: Application To the Icdow Modelmentioning

confidence: 99%

“…After solving the generalized eigenproblem ( 4) for the ICDOW model (see [2] for details) we obtain the eigenvalues…”

Section: Application To the Icdow Modelmentioning

confidence: 99%

“…In Figure 5 we present the bifurcation curves, i.e. inflection and coincidence loci, for ICDOW model with coefficient function ρ i appearing in [2]. We use the fractional function f w show in Figure 6 left.…”

Section: Application To the Icdow Modelmentioning

confidence: 99%

“…We study shock and rarefaction curves arising in systems of conservation laws in which there are states whose characteristic speeds coincide. Indeed, examples of such models are found in [18,2,1]. Furthermore, we take into account composite rarefaction-shock wave curves in situations in which analytical difficulties were not fully considered previously.…”

Section: Introductionmentioning

confidence: 99%

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Resonance in rarefaction and shock curves: Local analysis and numerics of the continuation method

Alvarez

Goedert

Marchesin

2020

J. Hyper. Differential Equations

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We describe certain crucial steps in the development of an algorithm for finding the Riemann solution to systems of conservation laws. We relax the classical hypotheses of strict hyperbolicity and genuine nonlinearity due to Lax. First, we present a procedure for continuing wave curves beyond points where characteristic speeds coincide, i.e. at wave curve points of maximal co-dimensionality. This procedure requires strict hyperbolicity on both sides of the coincidence locus. Loss of strict hyperbolicity is regularized by means of a Generalized Jordan Chain, which serves to construct a four-fold sub-manifold structure on which wave curves can be continued. Second, we analyze the loss of genuine nonlinearity. We prove a new result: the existence of composite wave curves when the composite wave traverses either the inflection locus or an anomalous part of the non-local composite wave curve. In this sense, we find conditions under which the composite field is well defined and its singularities can be removed, allowing use of our continuation method. Finally, we present numerical examples for a non-strictly hyperbolic system of conservation laws.

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“…In this section we exemplify the appearance of coincidence locus with the model studied in [2]. The procedure developed in this paper is used to solve a particular Riemann problem.…”

Section: Application To the Icdow Modelmentioning

confidence: 99%

“…After solving the generalized eigenproblem ( 4) for the ICDOW model (see [2] for details) we obtain the eigenvalues…”

Section: Application To the Icdow Modelmentioning

confidence: 99%

Section: Application To the Icdow Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations