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Numerical schemes provably preserving the positivity of density and pressure are highly desirable for ideal magnetohydrodynamics (MHD), but the rigorous positivity-preserving (PP) analysis remains challenging. The difficulties mainly arise from the intrinsic complexity of the MHD equations as well as the indeterminate relation between the PP property and the divergence-free condition on the magnetic field. This paper presents the first rigorous PP analysis of conservative schemes with the Lax--Friedrichs (LF) flux for 1D and multidimensional ideal MHD. The significant innovation is the discovery of the theoretical connection between the PP property and a discrete divergence-free (DDF) condition. This connection is established through the generalized LF splitting properties, which are alternatives to the usually expected LF splitting property that does not hold for ideal MHD. The generalized LF splitting properties involve a number of admissible states strongly coupled by the DDF condition, making their derivation very difficult. We derive these properties via a novel equivalent form of the admissible state set and an important inequality, which is skillfully constructed by technical estimates. Rigorous PP analysis is then presented for finite volume and discontinuous Galerkin schemes with the LF flux on uniform Cartesian meshes. In the 1D case, the PP property is proved for the first-order scheme with proper numerical viscosity, and also for arbitrarily high-order schemes under conditions accessible by a PP limiter. In the 2D case, we show that the DDF condition is necessary and crucial for achieving the PP property. It is observed that even slightly violating the proposed DDF condition may cause failure to preserve the positivity of pressure. We prove that the 2D LF type scheme with proper numerical viscosity preserves both the positivity and the DDF condition. Sufficient conditions are derived for 2D PP high-order schemes, and extension to 3D is discussed. Numerical examples provided in the supplementary material further confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper proposes the use of a specific combination of discrete and finite element methods for the simulation of systems of deformable bodies in order to reduce the computational cost, when certain assumptions can be made. In particular, the Updated Lagrangian finite element formulation and the central difference time integration method are employed together with certain simplifying assumptions in order to linearize this highly nonlinear contact problem and obtain solutions with realistic computational cost and sufficiently good accuracy. Furthermore, the paper discusses software implementation issues and the advantages that the Java technologies can offer in the development of such engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, we present a rigorous numerical analysis for a bounded artificial viscosity model (τ = μδσa(δ∥∇su∥F )∇su) for the numerical simulation of turbulent flows. In practice, the commonly used Smagorinsky model (τ = (csδ)2∥∇su∥F ∇su) is overly dissipative and yields unphysical results. To date, several methods for "clipping" the Smagorinsky viscosity have proven useful in improving the physical characteristics of the simulated flow. However, such heuristic strategies strongly rely upon a priori knowledge of the flow regime. The bounded artificial viscosity model relies on a highly nonlinear, but monotone and smooth, semilinear elliptic form for the artificial viscosity. For this model, we have introduced a variational computational strategy, provided finite element error convergence estimates, and included several computational examples indicating its improvement on the overly diffusive Smagorinsky model. [ABSTRACT FROM AUTHOR]

This article is concerned with the efficient and accurate simulation and optimization of linear Timoshenko beam networks subjected to external loads. A solution scheme based on analytic ansatz-functions known to provide analytic solutions for the deformation and rotation of a single beam with given boundary data is extended to the full network. It is demonstrated that the analytic approach is equivalent to a finite element (FE) method where only one element with a suitably chosen shape function per beam is required. The solution of the FE-type system provides analytic solutions at the nodes, from which the solutions along the beams can be reconstructed. Consequently analytic solutions for the network can be computed by a numerical scheme without applying a spacial discretization. While the assembly of the local stiffness matrices is slightly more expensive compared to an FE model using, e.g., linear ansatz-functions, the complexity of the solution of the FE-system is not. This is particularly interesting for topology and material optimization problems formulated on the network. In order to demonstrate the efficiency of the approach a numerical comparison to the case of linear ansatz-functions is provided followed by a series of studies with topology and multi-material optimization problems on networks. [ABSTRACT FROM AUTHOR]

Various research areas in the field of vehicle modelling, structural mechanics, engine dynamics, microelectromechanical systems (MEMS), etc. require the utilization of both multibody system formalism (MBS) and finite element method (FEM) in order to sufficiently capture the model's dynamics. The FEM-MBS coupling is accomplished by reducing the dimension of the FE-modelled part and then importing it into an MBS-code for further simulation. When using commercial FEM (Nastran, ANSYS, etc.) as well as MBS (SIMPACK) software packages the necessary standard input data (SID) file is needed for the coupling procedure (FEMBS interface). A problem arises by the restriction that both commercial FEM and MBS codes support only two condensation methods (Guyan reduction and component mode synthesis (CMS)), thus disabling the direct application of any other reduction approach (e.g. from the field of control theory) that actually could be better. In this article, the theoretical background of an implemented FEM-MBS interface (MORPACK) is presented allowing the application of any kind of reduction method for FE-modelled structures and furthermore their import (Ritz approximation) into SIMPACK via the SID file generation. A benchmark problem (UIC60-rail) is used in order to capture in SIMPACK the discrepancy between the standardized CMS and the Krylov subspace method (KSM), as one of the alternatives offered by the interface. [ABSTRACT FROM AUTHOR]