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In this paper we present a conservative cell-centered Lagrangian finite volume scheme for the solution of the hyper-elasticity equations on unstructured multidimensional grids. The starting point of the new method is the Eucclhyd scheme,…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a…
One of the limitations of the Lattice Boltzmann Method in simulating inertial flows is the coupling of the discretization of space to the velocity discretization. It requires an increase of the size of computational lattices in order to…
This study presents the development of a compact gas-kinetic scheme using an arbitrary Lagrangian-Eulerian (ALE) formulation for structured meshes. Unlike the Eulerian formulation, the ALE approach effectively tracks flow discontinuities,…
The Direct Simulation Monte Carlo (DSMC) method is widely employed for simulating rarefied nonequilibrium gas flows. With advances in aerospace engineering and micro/nano-scale technologies, gas flows exhibit the coexistence of rarefied and…
In this paper we present a new high order semi-implicit DG scheme on two-dimensional staggered triangular meshes applied to different nonlinear systems of hyperbolic conservation laws such as advection-diffusion models, incompressible…
A Lagrangian numerical scheme for solving nonlinear degenerate Fokker-Planck equations in space dimensions $d\ge2$ is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies…
We present a new high-order accurate Lagrangian discontinuous Galerkin (DG) hydrodynamic method to simulate material dynamics (for e.g., gasses, fluids, and solids) with up to fourth-order accuracy on cubic meshes. The variables, such as…
An efficient third-order discrete unified gas kinetic scheme (DUGKS) with efficiency is presented in this work for simulating continuum and rarefied flows. By employing two-stage time-stepping scheme and the high-order DUGKS flux…
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented by point clouds, eliminating the need for a global…
A novel smooth immersed boundary method (IBM) based on a direct-forcing formulation is proposed to simulate incompressible dense particle-laden flows. This IBM relies on a regularization of the transfer function between the Eulerian grid…
A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Non-ideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and…
We consider the incompressible three-dimensional Euler equations for a vortex ring with Kelvin waves undergoing radially expanding Lagrangian transport. To clarify the fundamental mechanisms underlying nonlinear scale-local deformations of…
We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries.…
Within the framework of the homogeneous non-linear Boltzmann equation, we present a new analytic method, without the intrinsic limitations of existing methods, for obtaining asymptotic solutions. This method permits extension of existing…
The analytical solution of the boundary problem on behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in a slab of the conducting medium is received. The kinetic Vlasov---Boltzmann…
We present a practical numerical method for evaluating the Lagrange multipliers necessary for maintaining a constrained linear geometry of particles in dynamical simulations. The method involves no iterations, and is limited in accuracy…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the…