A Truncation Error Based Mesh Adaption Metric for CFD

AbstractTo deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order $${{\mathcal {O}}}(h^2)$$ O ( h 2 ) . Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

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Truncation error estimates for two‐dimensional sampling series associated with the linear canonical transform

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7403 ◽

2021 ◽

Author(s):

Haiye Huo

Keyword(s):

Error Estimates ◽

Truncation Error ◽

Linear Canonical Transform ◽

Two Dimensional ◽

Sampling Series

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High-order compact LOD methods for solving high-dimensional advection equations

Computational and Applied Mathematics ◽

10.1007/s40314-021-01483-w ◽

2021 ◽

Vol 40 (3) ◽

Author(s):

Bo Hou ◽

Yongbin Ge

Keyword(s):

Truncation Error ◽

Three Dimensional ◽

Taylor Series Expansion ◽

High Order ◽

High Dimensional ◽

Analysis Method ◽

Order Accuracy ◽

Von Neumann ◽

One Dimensional ◽

Von Neumann Analysis

AbstractIn this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

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Hybrid high algebraic order two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives

International Journal of Modern Physics C ◽

10.1142/s0129183116500492 ◽

2016 ◽

Vol 27 (05) ◽

pp. 1650049 ◽

Cited By ~ 1

Author(s):

Junyan Ma ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Truncation Error ◽

Resonance Problem ◽

Phase Lag ◽

Step Method ◽

Algebraic Order ◽

Test Equation ◽

The Stability ◽

Scalar Test Equation

A hybrid tenth algebraic order two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives are obtained in this paper. We will investigate • the construction of the method • the local truncation error (LTE) of the newly obtained method. We will also compare the lte of the newly developed method with other methods in the literature (this is called the comparative LTE analysis) • the stability (interval of periodicity) of the produced method using frequency for the scalar test equation different from the frequency used in the scalar test equation for phase-lag analysis (this is called stability analysis) • the application of the newly obtained method to the resonance problem of the Schrödinger equation. We will compare its effectiveness with the efficiency of other known methods in the literature. It will be proved that the developed method is effective for the approximate solution of the Schrödinger equation and related periodical or oscillatory initial value or boundary value problems.

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CHARACTERIZATION OF IMAGE SPACE OF A WAVELET TRANSFORM

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691306001439 ◽

2006 ◽

Vol 04 (03) ◽

pp. 547-557 ◽

Cited By ~ 6

Author(s):

CAIXIA DENG ◽

YULING QU ◽

LIJUAN GU

Keyword(s):

Wavelet Transform ◽

Truncation Error ◽

Reproducing Kernel ◽

Reproducing Kernel Hilbert Space ◽

Sampling Theorem ◽

Image Space ◽

Kernel Space ◽

Reproducing Kernel Space ◽

Scope Of Application

In this paper, Journe wavelet function is introduced as a wavelet generating function. The expression of reproducing kernel function for the image space of this wavelet transform is obtained based on the fact that the image space of the wavelet transform is a reproducing kernel Hilbert space. Then the isometric identity of Journe wavelet transform is obtained. The connections between the image space of the wavelet transform and the image space of the known reproducing kernel space are established by the theories of reproducing kernel. The properties and the structures of the image space of the wavelet transform can be characterized by the properties and the structures of the image space of the known reproducing kernel space. Using the ideas of reproducing kernel, we consider there are relations between the wavelet transform and the sampling theorem. Meanwhile, the approximations in sampling theorems is shown and the truncation error is given. This provides a theoretical basis for us to study the image space of the general wavelet transform and broadens the scope of application of theories of the reproducing kernel space.

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