Related papers: Entropy-dissipating finite-difference schemes for …
We present a first order scheme based on a staggered grid for the shallow water equations with topography in two space dimensions, which enjoys several properties: positivity of the water height, preservation of constant states, and weak…
The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonlinear PDE models presents theoretical and numerical challenges…
We develop a structure-preserving numerical discretization for the electrostatic Euler-Poisson equations with a constant magnetic field. The scheme preserves positivity of the density, positivity of the internal energy and a minimum…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…
Consistency and stability are two essential ingredients in the design of numerical algorithms for partial differential equations. Robust algorithms can be developed by incorporating nonlinear physical stability principles in their design,…
Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new…
The one-dimensional modified shallow water equations in Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in Lagrangian coordinates, in mass Lagrangian variables, and Eulerian…
We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…
Under a precise nonlinearity-diffusivity assumption we establish the decay of entropy solutions of a degenerate nonlinear parabolic equation with initial data being a sum of periodic function and a function vanishing at infinity (in the…
In this paper, two finite difference numerical schemes are proposed and analyzed for the droplet liquid film model, with a singular Leonard-Jones energy potential involved. Both first and second order accurate temporal algorithms are…
First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite…
The dynamics of thermally fluctuating conserved order parameters are described by stochastic conservation laws. Thermal equilibrium in such systems requires the dissipative and stochastic components of the flux to be related by detailed…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
In this work we first prove, by formal arguments, that the diffusion limit of nonlinear kinetic equations, where both the transport term and the turning operator are density-dependent, leads to volume-exclusion chemotactic equations. We…
We propose a novel formulation for parametric finite element methods to simulate surface diffusion of closed curves, which is also called as the curve diffusion. Several high-order temporal discretizations are proposed based on this new…
The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and…
The paper describes the construction of entropy-stable discontinuous Galerkin difference (DGD) discretizations for hyperbolic conservation laws on unstructured grids. The construction takes advantage of existing theory for entropy-stable…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…