Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1697-1717, August 2024. Abstract. This paper shows both analytically and numerically that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate in a low-frequency regime. The non-Hermiticity is due to the introduction of a directional damping term (motivated by an imaginary gauge potential), which leads to a skin effect that is manifested by the system’s eigenmodes accumulating at one edge of the structure. We elucidate the topological protection of the associated (real) eigenfrequencies and illustrate numerically the competition between the two different localization effects present when the system is randomly perturbed: the non-Hermitian skin effect and the disorder-induced Anderson localization. We show numerically that, as the strength of the disorder increases, more and more eigenmodes become localized in the bulk. Our results are based on an asymptotic matrix model for subwavelength physics and can be generalized also to tight-binding models in condensed matter theory.
{"title":"Stability of the Non-Hermitian Skin Effect in One Dimension","authors":"Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu","doi":"10.1137/23m1610537","DOIUrl":"https://doi.org/10.1137/23m1610537","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1697-1717, August 2024. <br/> Abstract. This paper shows both analytically and numerically that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate in a low-frequency regime. The non-Hermiticity is due to the introduction of a directional damping term (motivated by an imaginary gauge potential), which leads to a skin effect that is manifested by the system’s eigenmodes accumulating at one edge of the structure. We elucidate the topological protection of the associated (real) eigenfrequencies and illustrate numerically the competition between the two different localization effects present when the system is randomly perturbed: the non-Hermitian skin effect and the disorder-induced Anderson localization. We show numerically that, as the strength of the disorder increases, more and more eigenmodes become localized in the bulk. Our results are based on an asymptotic matrix model for subwavelength physics and can be generalized also to tight-binding models in condensed matter theory.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"45 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1668-1696, August 2024. Abstract. Exploring the mechanism of phosphate ([math]) uptake by algae is essential to accurate prediction and a comprehensive understanding of harmful algal blooms (HABs). Previous experimental studies have revealed the existence of two distinct [math] pools, namely the surface-adsorbed [math] pool and the intracellular [math] pool, in certain species of algae. Motivated by these observations, a novel stoichiometric model, which incorporates a two-stage [math] uptake process, is proposed and analyzed to investigate the impact of these [math] pools on algal growth. Model validation results show that with proper parameterizations, this model can accurately capture algal growth dynamics in the laboratory and in the field. The asymptotic dynamics are explored through a complete mathematical analysis and the transient dynamics are explored through multiscale analysis, revealing the driving mechanism of different growth phases of algae. Furthermore, we derive an approximate formula for estimating the switching time from high to low growth rate in algae, which can serve as a valuable tool for predicting the duration of HABs. These findings contribute to the strengthening of prediction and improving understanding of HABs.
{"title":"Asymptotic and Transient Dynamics of a Stoichiometric Algal Growth Model with Two-Stage Phosphate Uptake","authors":"Shufei Gao, Sanling Yuan, Anglu Shen, Hao Wang","doi":"10.1137/23m1611750","DOIUrl":"https://doi.org/10.1137/23m1611750","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1668-1696, August 2024. <br/> Abstract. Exploring the mechanism of phosphate ([math]) uptake by algae is essential to accurate prediction and a comprehensive understanding of harmful algal blooms (HABs). Previous experimental studies have revealed the existence of two distinct [math] pools, namely the surface-adsorbed [math] pool and the intracellular [math] pool, in certain species of algae. Motivated by these observations, a novel stoichiometric model, which incorporates a two-stage [math] uptake process, is proposed and analyzed to investigate the impact of these [math] pools on algal growth. Model validation results show that with proper parameterizations, this model can accurately capture algal growth dynamics in the laboratory and in the field. The asymptotic dynamics are explored through a complete mathematical analysis and the transient dynamics are explored through multiscale analysis, revealing the driving mechanism of different growth phases of algae. Furthermore, we derive an approximate formula for estimating the switching time from high to low growth rate in algae, which can serve as a valuable tool for predicting the duration of HABs. These findings contribute to the strengthening of prediction and improving understanding of HABs.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"52 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141885388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1658-1667, August 2024. Abstract. In this paper, the classical problem of two-dimensional flow in a cylindrical domain, driven by a nonuniform tangential velocity imposed at the boundary, is reconsidered in straightforward manner. When the boundary velocity is a pure rotation [math] plus a small perturbation [math] and when the Reynolds number based on [math] is large (Re [math]), this flow is of “Prandtl–Batchelor” type, namely, a flow of uniform vorticity [math] in a core region inside a viscous boundary layer of thickness O(Re)[math]. The O[math] contribution to [math] is determined here by asymptotic analysis up to O[math]. The result is in good agreement with numerical computation for Re [math].
{"title":"Prandtl–Batchelor Flow in a Cylindrical Domain","authors":"Emmanuel Dormy, H. Keith Moffatt","doi":"10.1137/24m1637313","DOIUrl":"https://doi.org/10.1137/24m1637313","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1658-1667, August 2024. <br/> Abstract. In this paper, the classical problem of two-dimensional flow in a cylindrical domain, driven by a nonuniform tangential velocity imposed at the boundary, is reconsidered in straightforward manner. When the boundary velocity is a pure rotation [math] plus a small perturbation [math] and when the Reynolds number based on [math] is large (Re [math]), this flow is of “Prandtl–Batchelor” type, namely, a flow of uniform vorticity [math] in a core region inside a viscous boundary layer of thickness O(Re)[math]. The O[math] contribution to [math] is determined here by asymptotic analysis up to O[math]. The result is in good agreement with numerical computation for Re [math].","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"75 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141885389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1631-1657, August 2024. Abstract. This paper addresses the inverse scattering problem for Maxwell’s equations in three-dimensional anisotropic periodic media. We study a new imaging functional for the fast and robust reconstruction of the shape of anisotropic periodic scatterers from boundary measurements of the scattered field. The implementation of this imaging functional is simple and avoids the need to solve an ill-posed problem. The resolution and stability analysis of the imaging functional is investigated. Results from our numerical study indicate that this imaging functional is more stable than that of the factorization method and more accurate than that of the orthogonality sampling method in reconstructing periodic scatterers.
{"title":"A Stable Imaging Functional for Anisotropic Periodic Media in Electromagnetic Inverse Scattering","authors":"Dinh-Liem Nguyen, Trung Truong","doi":"10.1137/23m1577080","DOIUrl":"https://doi.org/10.1137/23m1577080","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1631-1657, August 2024. <br/> Abstract. This paper addresses the inverse scattering problem for Maxwell’s equations in three-dimensional anisotropic periodic media. We study a new imaging functional for the fast and robust reconstruction of the shape of anisotropic periodic scatterers from boundary measurements of the scattered field. The implementation of this imaging functional is simple and avoids the need to solve an ill-posed problem. The resolution and stability analysis of the imaging functional is investigated. Results from our numerical study indicate that this imaging functional is more stable than that of the factorization method and more accurate than that of the orthogonality sampling method in reconstructing periodic scatterers.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"30 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sebastian Acosta, Jesse Chan, Raven Johnson, Benjamin Palacios
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1609-1630, August 2024. Abstract. To strike a balance between modeling accuracy and computational efficiency for simulations of ultrasound waves in soft tissues, we derive a pseudodifferential factorization of the wave operator with fractional attenuation. This factorization allows us to approximately solve the Helmholtz equation via one-way (transmission) or two-way (transmission and reflection) sweeping schemes tailored to high-frequency wave fields. We provide explicitly the three highest order terms of the pseudodifferential expansion to incorporate the well-known square-root first order symbol for wave propagation, the zeroth order symbol for amplitude modulation due to changes in wave speed and damping, and the next symbol to model fractional attenuation. We also propose wide-angle Padé approximations for the pseudodifferential operators corresponding to these three highest order symbols. Our analysis provides insights regarding the role played by the frequency and the Padé approximations in the estimation of error bounds. We also provide a proof-of-concept numerical implementation of the proposed method and test the error estimates numerically.
{"title":"Pseudodifferential Models for Ultrasound Waves with Fractional Attenuation","authors":"Sebastian Acosta, Jesse Chan, Raven Johnson, Benjamin Palacios","doi":"10.1137/24m1634011","DOIUrl":"https://doi.org/10.1137/24m1634011","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1609-1630, August 2024. <br/> Abstract. To strike a balance between modeling accuracy and computational efficiency for simulations of ultrasound waves in soft tissues, we derive a pseudodifferential factorization of the wave operator with fractional attenuation. This factorization allows us to approximately solve the Helmholtz equation via one-way (transmission) or two-way (transmission and reflection) sweeping schemes tailored to high-frequency wave fields. We provide explicitly the three highest order terms of the pseudodifferential expansion to incorporate the well-known square-root first order symbol for wave propagation, the zeroth order symbol for amplitude modulation due to changes in wave speed and damping, and the next symbol to model fractional attenuation. We also propose wide-angle Padé approximations for the pseudodifferential operators corresponding to these three highest order symbols. Our analysis provides insights regarding the role played by the frequency and the Padé approximations in the estimation of error bounds. We also provide a proof-of-concept numerical implementation of the proposed method and test the error estimates numerically.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"58 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141778882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1557-1579, August 2024. Abstract. In this paper, taking into account the maturation period of prey, we propose a predator-prey model with time delay and fear effect. We confirm the well-posedness of the model system, explore the stability of the equilibria and uniform persistence of the model, and investigate Hopf bifurcations. Moreover, we also numerically explore the global continuation of the Hopf bifurcation. Interestingly, our results show that as the delay increases, the stable and unstable periodic solutions may both disappear and the unstable positive equilibrium may regain its stability. These results reveal how the maturation delay and the fear effect jointly impact the population dynamics of the predator-prey system.
{"title":"Joint Impact of Maturation Delay and Fear Effect on the Population Dynamics of a Predator-Prey System","authors":"Xiaoke Ma, Ying Su, Xingfu Zou","doi":"10.1137/23m1596569","DOIUrl":"https://doi.org/10.1137/23m1596569","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1557-1579, August 2024. <br/> Abstract. In this paper, taking into account the maturation period of prey, we propose a predator-prey model with time delay and fear effect. We confirm the well-posedness of the model system, explore the stability of the equilibria and uniform persistence of the model, and investigate Hopf bifurcations. Moreover, we also numerically explore the global continuation of the Hopf bifurcation. Interestingly, our results show that as the delay increases, the stable and unstable periodic solutions may both disappear and the unstable positive equilibrium may regain its stability. These results reveal how the maturation delay and the fear effect jointly impact the population dynamics of the predator-prey system.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"63 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1580-1608, August 2024. Abstract. We derive accurate, closed-form analytical approximations for the phase-plane trajectories of the standard susceptible-infectious-removed (SIR) epidemic model, including host births and deaths, giving a complete description of the transient dynamics. Our approximations for the SIR ordinary differential equations also allow us to provide convenient, accurate analytical approximations for the associated Poincaré map, and the minimum and maximum susceptible and infectious host densities in each epidemic wave. Our analysis involves matching asymptotic expansions across branch cuts of the Lambert [math] function.
{"title":"Uniform Asymptotic Approximations for the Phase Plane Trajectories of the SIR Model with Vital Dynamics","authors":"Todd L. Parsons, David J. D. Earn","doi":"10.1137/23m1576050","DOIUrl":"https://doi.org/10.1137/23m1576050","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1580-1608, August 2024. <br/> Abstract. We derive accurate, closed-form analytical approximations for the phase-plane trajectories of the standard susceptible-infectious-removed (SIR) epidemic model, including host births and deaths, giving a complete description of the transient dynamics. Our approximations for the SIR ordinary differential equations also allow us to provide convenient, accurate analytical approximations for the associated Poincaré map, and the minimum and maximum susceptible and infectious host densities in each epidemic wave. Our analysis involves matching asymptotic expansions across branch cuts of the Lambert [math] function.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"94 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141778881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1504-1514, August 2024. Abstract. We introduce a simple mathematical model for bushfires accounting for temperature diffusion in the presence of a combustion term which is activated above a given ignition state. The model also takes into consideration the effect of the environmental wind and of the pyrogenic flow. The simplicity of the model is highlighted by the fact that it is described by a single scalar equation, containing only four terms, making it very handy for rapid and effective numerical simulations which run in real time. In spite of its simplicity, the model is in agreement with data collected from bushfire experiments in the lab, as well as with spreading of bushfires that have been observed in the real world. Moreover, the equation describing the temperature evolution can be easily linked to a geometric evolution problem describing the level sets of the ignition state.
{"title":"A Simple but Effective Bushfire Model: Analysis and Real-Time Simulations","authors":"Serena Dipierro, Enrico Valdinoci, Glen Wheeler, Valentina-Mira Wheeler","doi":"10.1137/24m1644596","DOIUrl":"https://doi.org/10.1137/24m1644596","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1504-1514, August 2024. <br/> Abstract. We introduce a simple mathematical model for bushfires accounting for temperature diffusion in the presence of a combustion term which is activated above a given ignition state. The model also takes into consideration the effect of the environmental wind and of the pyrogenic flow. The simplicity of the model is highlighted by the fact that it is described by a single scalar equation, containing only four terms, making it very handy for rapid and effective numerical simulations which run in real time. In spite of its simplicity, the model is in agreement with data collected from bushfire experiments in the lab, as well as with spreading of bushfires that have been observed in the real world. Moreover, the equation describing the temperature evolution can be easily linked to a geometric evolution problem describing the level sets of the ignition state.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"25 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Philipp Dönges, Thomas Götz, Nataliia Kruchinina, Tyll Krüger, Karol Niedzielewski, Viola Priesemann, Moritz Schäfer
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1460-1481, August 2024. Abstract. Households play an important role in disease dynamics. Many infections happen there due to the close contact, while mitigation measures mainly target the transmission between households. Therefore, one can see households as boosting the transmission depending on household size. To study the effect of household size and size distribution, we differentiated within and between household reproduction rates. There are basically no preventive measures, and thus the close contacts can boost the spread. We explicitly incorporated that typically only a fraction of all household members are infected. Thus, viewing the infection of a household of a given size as a splitting process generating a new small fully infected subhousehold and a remaining still susceptible subhousehold, we derive a compartmental ODE model for the dynamics of the subhouseholds. In this setting, the basic reproduction number as well as prevalence and the peak of an infection wave in a population with given household size distribution can be computed analytically. We compare numerical simulation results of this novel household ODE model with results from an agent-based model using data for realistic household size distributions of different countries. We find good agreement of both models showing the catalytic effect of large households on the overall disease dynamics.
{"title":"SIR Model for Households","authors":"Philipp Dönges, Thomas Götz, Nataliia Kruchinina, Tyll Krüger, Karol Niedzielewski, Viola Priesemann, Moritz Schäfer","doi":"10.1137/23m1556861","DOIUrl":"https://doi.org/10.1137/23m1556861","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1460-1481, August 2024. <br/> Abstract. Households play an important role in disease dynamics. Many infections happen there due to the close contact, while mitigation measures mainly target the transmission between households. Therefore, one can see households as boosting the transmission depending on household size. To study the effect of household size and size distribution, we differentiated within and between household reproduction rates. There are basically no preventive measures, and thus the close contacts can boost the spread. We explicitly incorporated that typically only a fraction of all household members are infected. Thus, viewing the infection of a household of a given size as a splitting process generating a new small fully infected subhousehold and a remaining still susceptible subhousehold, we derive a compartmental ODE model for the dynamics of the subhouseholds. In this setting, the basic reproduction number as well as prevalence and the peak of an infection wave in a population with given household size distribution can be computed analytically. We compare numerical simulation results of this novel household ODE model with results from an agent-based model using data for realistic household size distributions of different countries. We find good agreement of both models showing the catalytic effect of large households on the overall disease dynamics.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"27 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1439-1459, August 2024. Abstract. Nonlinear conservation laws such as the system of ideal magnetohydrodynamics (MHD) equations may develop singularities over time. In these situations, viscous regularization is a common approach to regain regularity of the solution. In this paper, we present a new viscous flux to regularize the MHD equations that holds many attractive properties. In particular, we prove that the proposed viscous flux preserves positivity of density and internal energy, satisfies the minimum entropy principle, is consistent with all generalized entropies, and is Galilean and rotationally invariant. We also provide a variation of the viscous flux that conserves angular momentum. To make the analysis more useful for numerical schemes, the divergence of the magnetic field is not assumed to be zero. Using continuous finite elements, we show several numerical experiments, including contact waves and magnetic reconnection.
{"title":"Viscous Regularization of the MHD Equations","authors":"Tuan Anh Dao, Lukas Lundgren, Murtazo Nazarov","doi":"10.1137/23m1564274","DOIUrl":"https://doi.org/10.1137/23m1564274","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1439-1459, August 2024. <br/> Abstract. Nonlinear conservation laws such as the system of ideal magnetohydrodynamics (MHD) equations may develop singularities over time. In these situations, viscous regularization is a common approach to regain regularity of the solution. In this paper, we present a new viscous flux to regularize the MHD equations that holds many attractive properties. In particular, we prove that the proposed viscous flux preserves positivity of density and internal energy, satisfies the minimum entropy principle, is consistent with all generalized entropies, and is Galilean and rotationally invariant. We also provide a variation of the viscous flux that conserves angular momentum. To make the analysis more useful for numerical schemes, the divergence of the magnetic field is not assumed to be zero. Using continuous finite elements, we show several numerical experiments, including contact waves and magnetic reconnection.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"9 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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