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Communications in Applied and Industrial Mathematics
Journal Prestige (SJR): 0.324

Citation Impact (citeScore): 1
Number of Followers: 1

This is an Open Access Journal

Open Access journal
ISSN (Online) 2038-0909
Published by Sciendo

[370 journals]

High order Finite Difference/Discontinuous Galerkin schemes for the
incompressible Navier-Stokes equations with implicit viscosity
- Abstract: In this work we propose a novel numerical method for the solution of the incompressible Navier-Stokes equations on Cartesian meshes in 3D. The semi-discrete scheme is based on an explicit discretization of the nonlinear convective flux tensor and an implicit treatment of the pressure gradient and viscous terms. In this way, the momentum equation is formally substituted into the divergence-free constraint, thus obtaining an elliptic equation on the pressure which eventually maintains at the discrete level the involution on the divergence of the velocity field imposed by the governing equations. This makes our method belonging to the class of so-called structure-preserving schemes. High order of accuracy in space is achieved using an efficient CWENO reconstruction operator that is exploited to devise a conservative finite difference scheme for the convective terms. Implicit central finite differences are used to remove the numerical dissipation in the pressure gradient discretization. To avoid the severe time step limitation induced by the viscous eigenvalues related to the parabolic terms in the governing equations, we propose to devise an implicit local discontinuous Galerkin (DG) solver. The resulting viscous sub-system is symmetric and positive definite, therefore it can be efficiently solved at the aid of a matrix-free conjugate gradient method. High order in time is granted by a semi-implicit IMEX time stepping technique. Convergence rates up to third order of accuracy in space and time are proven, and a suite of academic benchmarks is shown in order to demonstrate the robustness and the validity of the novel schemes, especially in the context of high viscosity coefficients.
  PubDate: Mon, 27 Jun 2022 00:00:00 GMT
Recent Trends on Nonlinear Filtering for Inverse Problems
- Abstract: Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in view of the limit for infinitely particles and extensions towards stability analysis and multi–objective optimization. We illustrate the performance of the method by using test inverse problems from the literature.
  PubDate: Sun, 22 May 2022 00:00:00 GMT
Polynomial mapped bases: theory and applications
- Abstract: In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge’s and Gibbs effects.
  PubDate: Mon, 16 May 2022 00:00:00 GMT
Fluid-structure interaction simulations with a LES filtering approach in
- Abstract: The goal of this paper is to test solids4Foam, the fluid-structure interaction (FSI) toolbox developed for foam-extend (a branch of OpenFOAM), and assess its flexibility in handling more complex flows. For this purpose, we consider the interaction of an incompressible fluid described by a Leray model with a hyperelastic structure modeled as a Saint Venant-Kirchho material. We focus on a strongly coupled, partitioned fluid-structure interaction (FSI) solver in a finite volume environment, combined with an arbitrary Lagrangian-Eulerian approach to deal with the motion of the fluid domain. For the implementation of the Leray model, which features a nonlinear differential low-pass filter, we adopt a three-step algorithm called Evolve-Filter-Relax. We validate our approach against numerical data available in the literature for the 3D cross flow past a cantilever beam at Reynolds number 100 and 400.
  PubDate: Tue, 10 Aug 2021 00:00:00 GMT
Double-stage discretization approaches for biomarker-based bladder cancer
survival modeling
- Abstract: Bioinformatic techniques targeting gene expression data require specific analysis pipelines with the aim of studying properties, adaptation, and disease outcomes in a sample population. Present investigation compared together results of four numerical experiments modeling survival rates from bladder cancer genetic profiles. Research showed that a sequence of two discretization phases produced remarkable results compared to a classic approach employing one discretization of gene expression data. Analysis involving two discretization phases consisted of a primary discretizer followed by refinement or pre-binning input values before the main discretization scheme. Among all tests, the best model encloses a sequence of data transformation to compensate skewness, data discretization phase with class-attribute interdependence maximization algorithm, and final classification by voting feature intervals, a classifier that also provides discrete interval optimization.
  PubDate: Tue, 10 Aug 2021 00:00:00 GMT
Numerical methods for a system of coupled Cahn-Hilliard equations
- Abstract: In this work, we consider a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. We propose some numerical methods to approximate the solution of the system which are based on suitable combinations of existing schemes for the single Cahn-Hilliard equation. As a verification for our experimental approach, we present some tests and a detailed description of the numerical solutions’ behaviour obtained by varying the values of the system’s characteristic parameters.
  PubDate: Tue, 30 Mar 2021 00:00:00 GMT
A new two-component approach in modeling red blood cells
- Abstract: This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, will be done through adhesion forces adapting e cient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0.3 nm) is much smaller than the overall size (≃ 8000 nm). In this paper we display some numerical simulations that show how our approach can describe the interaction of an RBC with an exogenous body as well as the relaxation of the shape of an RBC toward its equilibrium configuration in absence of external forces.
  PubDate: Sat, 31 Oct 2020 00:00:00 GMT

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