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Ja E Ryong Kweon - One of the best experts on this subject based on the ideXlab platform.
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A numerical scheme for approximating interior Jump Discontinuity solution of a compressible Stokes system
Journal of Computational and Applied Mathematics, 2019Co-Authors: Joo Hyeong Han, Ja E Ryong KweonAbstract:Abstract In this paper we develop a numerical scheme for approximating interior Jump Discontinuity solutions of compressible Stokes flows with inflow Jump datum. The scheme is based on a decomposition of the velocity vector into three parts: the Jump part, an auxiliary one and the smoother one. The Jump Discontinuity is handled by constructing a vector function extending the density Jump value of the normal vector on the interface to the whole domain. We show existence of the finite element solutions for the three parts, derive error estimates and also convergence rates based on the piecewise regularities. Numerical examples are given, confirming the derived convergence rates.
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Compressible Navier-Stokes Equations in a Polyhedral Cylinder with Inflow Boundary Condition
Journal of Mathematical Fluid Mechanics, 2017Co-Authors: Oh Sung Kwon, Ja E Ryong KweonAbstract:In this paper our concern is with singularity and regularity of the compressible flows through a non-convex edge in \({\mathbb {R}}^3\). The flows are governed by the compressible Navies-Stokes equations on the infinite cylinder that has the non-convex edge on the inflow boundary. We split the edge singularity by the Poisson problem from the velocity vector and show that the remainder is twice differentiable while the edge singularity is observed to be propagated into the interior of the cylinder by the transport character of the continuity equation. An interior surface layer starting at the edge is generated and not Lipshitz continuous due to the singularity. The density function shows a very steep change near the interface and its normal derivative has a Jump Discontinuity across there.
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A Jump Discontinuity of compressible viscous flows grazing a non-convex corner
Journal de Mathématiques Pures et Appliquées, 2013Co-Authors: Ja E Ryong KweonAbstract:Abstract We show existence and regularity of solution for the compressible viscous steady state Navier–Stokes system on a polygon having a grazing corner and that the density has a Jump Discontinuity across a curve inside the domain. There are corresponding Jumps in derivatives of the velocity. The solution comes from a well-posed boundary value problem on a polygonal domain with a non-convex corner. A formula for the decay of the Jump is given. The decay formula suggests that density Jumps can occur in a compressible flow with a non-vanishing viscosity.
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A discontinuous solution for an evolution compressible stokes system in a bounded domain
Journal of Differential Equations, 2005Co-Authors: Ja E Ryong Kweon, Minsu SongAbstract:Abstract An evolution compressible Stokes system is studied in a bounded cylindrical region Q = Ω × ( 0 , T ) . The initial datum of pressure is assumed to have a Jump at a specified curve C 0 in Ω . As predicted by the Rankine–Hugoniot conditions, the pressure and velocity derivatives have Jump discontinuities along the characteristic plane of the curve C 0 directed by an ambient velocity vector. An explicit formula for the Jump Discontinuity is presented. The Jump decays exponentially in time, more rapidly for smaller viscosities. Under suitable conditions of the data, a regularity of the solution is established in a compact subregion of Q away from the Jump plane.
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Numerical simulations of Jump Discontinuity solutions for compressible Stokes flows
Communications in Nonlinear Science and Numerical Simulation, 1Co-Authors: Joo Hyeong Han, Ja E Ryong KweonAbstract:Abstract It has been shown in [8] that the solutions of compressible Stokes flows with inflow Jump condition can be decomposed into the Jump Discontinuity part (due to the pressure Jump) plus the contact singularity (to the boundary) plus the smoother one, which is twice differentiable. In this paper we design a numerical scheme of each part in the decomposition and numerically demonstrate its essential role for capturing the Jump Discontinuity behaviors of the solutions. Several numerical simulations are presented, describing the critical role of each part. It is thought that such algorithm is new in constructing the Jump Discontinuity solutions.
Izumi Takagi - One of the best experts on this subject based on the ideXlab platform.
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Stable patterns with Jump Discontinuity in systems with Turing instability and hysteresis
Discrete & Continuous Dynamical Systems - A, 2017Co-Authors: Steffen Härting, Anna Marciniak-czochra, Izumi TakagiAbstract:Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that equilibrium. In this paper we show that coupling reaction-diffusion equations with ordinary differential equations (ODE) may lead to a novel pattern formation phenomenon in which DDI causes destabilization of both constant solutions and Turing patterns. Bistability and hysteresis effects in the null sets of model nonlinearities yield formation of far from the equilibrium patterns with Jump Discontinuity. We derive conditions for stability of stationary solutions with Jump Discontinuity in a suitable topology which allows us to include the Discontinuity points and leads to the definition of \begin{document}$(\varepsilon_0, A)$\end{document} -stability. Additionally, we provide conditions on stability of patterns in a quasi-stationary model reduction. The analysis is illustrated on the example of three-component model of receptor-ligand binding. The proposed model provides an example of a mechanism of de novo formation of far from the equilibrium patterns in reaction-diffusion-ODE models involving co-existence of DDI and hysteresis.
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Stable patterns with Jump Discontinuity in systems with Turing instability and hysteresis
arXiv: Analysis of PDEs, 2015Co-Authors: Steffen Härting, Anna Marciniak-czochra, Izumi TakagiAbstract:Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that equilibrium. In this paper we show that coupling reaction-diffusion equations with ordinary differential equations (ODE) may lead to a novel pattern formation phenomenon in which DDI causes destabilization of both constant solutions and Turing patterns. Bistability and hysteresis effects in the null sets of model nonlinearities yield formation of far from the equilibrium patterns with Jump Discontinuity. We derive conditions for stability of stationary solutions with Jump Discontinuity in a suitable topology which allows disclosing the Discontinuity points and leads to the definition of ({\epsilon}0 , A)-stability. Additionally, we provide conditions on stability of patterns in a quasi-stationary model reduction. The analysis is illustrated on the example of three-component model of receptor-ligand binding. The proposed model provides an example of a mechanism of de novo formation of far from the equilibrium patterns in reaction-diffusion-ODE models involving co-existence of DDI and hysteresis.
Joo Hyeong Han - One of the best experts on this subject based on the ideXlab platform.
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A numerical scheme for approximating interior Jump Discontinuity solution of a compressible Stokes system
Journal of Computational and Applied Mathematics, 2019Co-Authors: Joo Hyeong Han, Ja E Ryong KweonAbstract:Abstract In this paper we develop a numerical scheme for approximating interior Jump Discontinuity solutions of compressible Stokes flows with inflow Jump datum. The scheme is based on a decomposition of the velocity vector into three parts: the Jump part, an auxiliary one and the smoother one. The Jump Discontinuity is handled by constructing a vector function extending the density Jump value of the normal vector on the interface to the whole domain. We show existence of the finite element solutions for the three parts, derive error estimates and also convergence rates based on the piecewise regularities. Numerical examples are given, confirming the derived convergence rates.
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Numerical simulations of Jump Discontinuity solutions for compressible Stokes flows
Communications in Nonlinear Science and Numerical Simulation, 1Co-Authors: Joo Hyeong Han, Ja E Ryong KweonAbstract:Abstract It has been shown in [8] that the solutions of compressible Stokes flows with inflow Jump condition can be decomposed into the Jump Discontinuity part (due to the pressure Jump) plus the contact singularity (to the boundary) plus the smoother one, which is twice differentiable. In this paper we design a numerical scheme of each part in the decomposition and numerically demonstrate its essential role for capturing the Jump Discontinuity behaviors of the solutions. Several numerical simulations are presented, describing the critical role of each part. It is thought that such algorithm is new in constructing the Jump Discontinuity solutions.
Sheerin Kayenat - One of the best experts on this subject based on the ideXlab platform.
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Applications of modified Mickens-type NSFD schemes to Lane–Emden equations
Computational and Applied Mathematics, 2020Co-Authors: Amit K. Verma, Sheerin KayenatAbstract:If there is a Jump Discontinuity present in the forcing term of a boundary value problem (BVP), the nonstandard finite difference (NSFD) and finite difference (FD) methods do not approximate the solutions very well. Here we use fuzzy transforms (FTs) and derive fuzzy transformed NSFD schemes that are referred to as non-standard fuzzy transform methods (NFTMs). The convergence of the derived NFTMs is established. Numerical solutions of Lane–Emden type equations are obtained using NFTMs. We show that NFTMs provide better results than NSFD and FD methods when the forcing term has a Jump Discontinuity. Even for large Jumps, the NFTMs provide more accurate results than the other methods.
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A note on the convergence of fuzzy transformed finite difference methods
Journal of Applied Mathematics and Computing, 2020Co-Authors: Amit K. Verma, Sheerin KayenatAbstract:In this paper, we develop numerical methods based on the fuzzy transform methods (FTMs). In this approach we apply fuzzy transforms on discrete version of the derivatives and use it to derive FTMs. We also establish convergence of the proposed FTMs. To test the efficiency of the proposed FTMs, we apply the FTM schemes on the second order nonlinear singular boundary value problems and fourth order BVPs. We allow the source term of the differential equation to have Jump Discontinuity and study the effect of Jump on FTMs and finite difference methods. The work shows that FTMs are better for both class of BVPs considered in this paper, having singularity, nonlinearity and Jump Discontinuity.
J N Reddy - One of the best experts on this subject based on the ideXlab platform.
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modeling of delamination in composite laminates using a layer wise plate theory
International Journal of Solids and Structures, 1991Co-Authors: Ever J Barbero, J N ReddyAbstract:Abstract The layer-wise laminate theory of Reddy is extended to account for multiple delaminations between layers, and the associated computational model is developed. Delaminations between layers of composite plates are modeled by Jump Discontinuity conditions at the interfaces. Geometric nonlinearity is included to capture layer buckling. The strain energy release rate distribution along the boundary of delaminations is computed by a novel algorithm. The computational model presented is validated through several numerical examples.
