lingfengfly.github.io/index.xml at master · lingfengfly/lingfengfly.github.io · GitHub

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    <title>Su&#39;s Blog</title>
    <link>https://lingfengfly.github.io/</link>
    <description>Recent content on Su&#39;s Blog</description>
    <generator>Hugo -- gohugo.io</generator>
    <language>c/c&#43;&#43;, python, matlab</language>
    <copyright>&amp;copy;lingfengfly 2015-2020</copyright>
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    <item>
      <title>About</title>
      <link>https://lingfengfly.github.io/numerical/about/</link>
      <pubDate>Sun, 01 Mar 2020 13:02:40 +0800</pubDate>

      <guid>https://lingfengfly.github.io/numerical/about/</guid>
      <description>该目录下的内容主要是关于数值计算。 The content under this menu is mainly about the numerical computing. Please be free to correct my error.</description>
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    <item>
      <title></title>
      <link>https://lingfengfly.github.io/numerical/Finite-Volume-Method/About/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>

      <guid>https://lingfengfly.github.io/numerical/Finite-Volume-Method/About/</guid>
      <description>有限体积法（Fininte Volume Method, FVM）是一种基于守恒律的数值解法。 FVM将求解区域离散为网格（可以是结构化也可以是非结构化类型），然后将其划</description>
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      <title></title>
      <link>https://lingfengfly.github.io/posts/about/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>

      <guid>https://lingfengfly.github.io/posts/about/</guid>
      <description>write about something!</description>
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    <item>
      <title>Acoustics boundary</title>
      <link>https://lingfengfly.github.io/numerical/Finite-Volume-Method/Acoustics-boundary/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>

      <guid>https://lingfengfly.github.io/numerical/Finite-Volume-Method/Acoustics-boundary/</guid>
      <description>The systems of equations, such as acoustics, can have positive and negative eigenvalues, so that each boundary will typiccally have both incoming and outcoming characteristics.
Consider the acoustics equations
$$ p_t+K_0u_x=0 $$ $$ \rho_0u_t+p_x=0, $$ with a variety of different boundary conditions.
1.Nonreflecting Boundary Conditions
We want to impose nonreflectiong boundary conditions (absorbing boundary conditions) at points $x=a$ and $x=b$ that do not introduce spurious reflections of the outgoing acoustic waves.</description>
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      <title>Convergence</title>
      <link>https://lingfengfly.github.io/numerical/Finite-Volume-Method/Convergence/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>

      <guid>https://lingfengfly.github.io/numerical/Finite-Volume-Method/Convergence/</guid>
      <description>For a finite volume method, we might want to compare $Q^n_1$ with
$$\begin{equation}q^n_i=\frac {1}{\Delta x}\int_{x_{i-1/2}}^{x_{i+1/2}} q(x,t_n) \,{\rm d}x.\end{equation}$$If the function $q(x,t)$ is sufficiently smooth, then the pointwise value agrees with the cell average to $\cal O(\Delta x^2)$. It is reasonable to assume that the ratio $\Delta t/\Delta x$ is fixed. Then we can speak of letting $\Delta t \to 0$ to refine the grid, and speak of convergence with order s if the errors vanish like $\cal O(\Delta t^s)$ or $\cal O(\Delta x^s)$.</description>
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