DatabaseFactory.cs

public static class DatabaseFactory
{
    private static ISqlLocalDbInstance GetInstance()
    {
        var provider = new SqlLocalDbProvider();
        return provider.GetInstance("v13.0");
    }

    public static IDatabase CreateDatabase()
    {
        var instance = GetInstance();
        var dbName = Guid.NewGuid().ToString("N");

        instance.Start();

        var builder = instance.CreateConnectionStringBuilder();
        builder.SetInitialCatalogName(dbName);
        var connectionString = builder.ConnectionString;

        return new TestDatabase(instance, dbName);
    }

    private class TestDatabase : IDatabase
    {
        private readonly ISqlLocalDbInstance instance;

        public TestDatabase(ISqlLocalDbInstance dbInstance, string dbName)
        {
            instance = dbInstance;
            Name = dbName;
        }

        public string Name { get; }

        public DbConnection CreateConnection()
        {
            var builder = instance.CreateConnectionStringBuilder();
            builder.InitialCatalog = Name;
            return new SqlConnection(builder.ConnectionString);
        }

        public void Dispose()
        {
            instance.DropDatabase(Name);
        }
    }
}

IDatabase.cs

public interface IDatabase : IDisposable
{
    string Name { get; }

    DbConnection CreateConnection();
}

SqlLocalDbInstanceExtensions.cs

internal static class SqlLocalDbInstanceExtensions
{
    public static void CreateDatabase(this ISqlLocalDbInstance instance, string name)
    {
        if (instance == null)
            throw new ArgumentNullException(nameof(instance));

        if (string.IsNullOrEmpty(name))
            throw new ArgumentException("Value cannot be null or empty", nameof(name));

        var fileName = Path.Combine(Environment.CurrentDirectory, name + ".mdf");

        using (var connection = instance.CreateConnection())
        {
            connection.Open();
            using (var command = connection.CreateCommand())
            {
                command.CommandText =
                    Invariant($"CREATE DATABASE [{name}] on (name='{name}', filename='{fileName}');");

                command.ExecuteNonQuery();
            }
        }
    }

    public static void DropDatabase(this ISqlLocalDbInstance instance, string name)
    {
        if (instance == null)
            throw new ArgumentNullException(nameof(instance));

        if (string.IsNullOrEmpty(name))
            return;

        using (var connection = instance.CreateConnection())
        {
            connection.Open();
            using (var command = connection.CreateCommand())
            {
                command.CommandText =
                    Invariant($"ALTER DATABASE [{name}] SET SINGLE_USER WITH ROLLBACK IMMEDIATE; DROP DATABASE [{name}];");

                command.ExecuteNonQuery();
            }
        }
    }
}