This paper summarizes suitable material models for creep and damage of concrete which are coupled with heat and moisture transfer. The fully coupled approach or the staggered coupling is assumed. Governing equations are spatially dis-cretized by the finite element method and the temporal discretization is done by the generalized trapezoidal method. Systems of non-linear algebraic equations are solved by the Newton method. Development of an efficient and extensible computer code based on the C++ programming language is described. Finally, successful analyses of two real engineering problems are described.

An unstructured nodal spectral-element method for the Navier-Stokes equations is developed in this paper. The method is based on a triangular and tetrahedral rational approximation and an easy-to-implement nodal basis which fully enjoys the tensorial product property. It allows arbitrary triangular and tetrahedral mesh, affording greater flexibility in handling complex domains while maintaining all essential features of the usual spectral-element method. The details of the implementation and some numerical examples are provided to validate the efficiency and flexibility of the proposed method.

We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form. It applies in multidimensional structured and unstructured meshes. The proposed method is an extension of the UFORCE method developed by Stecca, Siviglia and Toro, in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann fan. The proposed first-order method is shown to be identical to the Godunov upwind method in applications to a 2 x 2 linear hyperbolic system. The method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water equations. Extension to second-order accuracy is carried out using an ADER-WENO approach in the finite volume framework on unstructured meshes. Finally, numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.

Solving elasticity equations with interfaces is a challenging problem for most existing methods. Nonetheless, it has wide applications in engineering and science. An accurate and efficient method is desired. In this paper, an efficient non-traditional finite element method with non-body-fitting grids is proposed to solve elasticity equations with interfaces. The main idea is to choose the test function basis to be the standard finite element basis independent of the interface and to choose the solution basis to be piecewise linear satisfying the jump conditions across the interface. The resulting linear system of equations is shown to be positive definite under certain assumptions. Numerical experiments show that this method is second order accurate in the L∞ norm for piecewise smooth solutions. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interface corner.

We present a parallel Cartesian method to solve elliptic problems with complex immersed interfaces. This method is based on a finite-difference scheme and is second-order accurate in the whole domain. The originality of the method lies in the use of additional unknowns located on the interface, allowing to express straightforwardly the interface transmission conditions. We describe the method and the details of its parallelization performed with the PETSc library. Then we present numerical validations in two dimensions, assorted with comparisons to other related methods, and a numerical study of the parallelized method.

The Cubic-Polynomial Interpolation scheme has been developed and applied to many practical simulations. However, it seems the existing Cubic-Polynomial Interpolation scheme are restricted to uniform rectangular meshes. Consequently, this scheme has some limitations to problems in irregular domains. This paper will extend the Cubic-Polynomial Interpolation scheme to triangular meshes by using some spline interpolation techniques. Numerical examples are provided to demonstrate the accuracy of the proposed schemes.

A unified process for the construction of hierarchical conforming bases on a range of element types is proposed based on an ab initio preservation of the underlying cohomology. This process supports not only the most common simplicial element types, as are now well known, but is generalized to squares, hexahedra, prisms and importantly pyramids. Whilst these latter cases have received (to varying degrees) attention in the literature, their foundation is less well developed than for the simplicial case. The generalization discussed in this paper is effected by recourse to basic ideas from algebraic topology (differential forms, homology, cohomology, etc) and as such extends the fundamental theoretical framework established by the work of Hiptmair and Arnold et al. for simplices. The process of forming hierarchical bases involves a recursive orthogonalization and it is shown that the resulting finite element mass, quasi-stiffness and composite matrices exhibit exponential or better growth in condition number.

First introduced in, the lumped particle framework is a flexible and numerically efficient framework for the modelling of particle transport in fluid flow. In this paper, the framework is expanded to simulate multicomponent particle-laden fluid flow. This is accomplished by introducing simulation protocols to model particles over a wide range of length and time scales. Consequently, we present a time ordering scheme and an approximate approach for accelerating the computation of evolution of different particle constituents with large differences in physical scales. We apply the extended framework on the temporal evolution of three particle constituents in sandladen flow, and horizontal release of spherical particles. Furthermore, we evaluate the numerical error of the lumped particle model. In this context, we discuss the Velocity-Verlet numerical scheme, and show how to apply this to solving Newton’s equations within the framework. We show that the increased accuracy of the Velocity-Verlet scheme is not lost when applied to the lumped particle framework.

Three high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers for different convective Mach numbers ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method of Yee & Sjögreen is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results compiled by Barone et al., and published direct numerical simulations (DNS) work of Rogers & Moser and Pantano & Sarkar, whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.

This paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave number. Rigorous matrix analysis is conducted in investigations and the oscillation-free computational procedure is proven to be stable in an asymptotic sense. Simulated examples are given to illustrate the conclusion.